Russian Mathematical Surveys, 2022, Volume 77, Issue 3, Pages 559–569 DOI: https://doi.org/10.1070/RM10043 (Mi rm10043)

DOI: https://doi.org/10.1070/RM10043

Bibliographic databases:

Zoom inZoom out

The remarkable mathematician, corresponding member of the Russian Academy of Sciences, principal researcher in the Department of Geometry and Topology of the Steklov Mathematical Institute Evgenii Vital’evich Shchepin observed his 70th birthday.

He was born on October 10, 1951, in the village of Ashukino in Moscow Oblast. His parents Anna Konstantinovna and Vitaly Sergeevich were school teachers of mathematics. His mother was born in Stavropol Region and his father in the Vyatka Oblast. In 1965 Shchepin’s family moved to Pushkino, Moscow Oblast. In the next year Evgeny Shchepin, as a winner of the Moscow Mathematical Olympiad, was sent to the Kolmogorov boarding school (formerly Physical and Mathematical School no. 18 and now the Advanced Educational Scientific Center of Moscow State University) by the City Department of Public Education.

The Kolmogorov boarding school, which was opened in 1963, had its heyday in those years. The competition for admission was about thirty contenders per place. Shchepin was one of the best students in physics in his year. He won an olympiad at the Moscow Institute of Physics and Technology and was going to enroll in this institute after graduating from school. However, at the last minute he changed his mind and enrolled in the Faculty of Mechanics and Mathematics of Moscow State University.

His scientific career in mathematics began with P. S. Alexandroff as his scientific advisor. During his student years, he published 10 research articles; the first was published in 1970. In 1976, he was awarded the Prize for Young Mathematicians of the Moscow Mathematical Society for his work “Topology of limit spaces of uncountable inverse spectra” [5]. Since 1977, Shchepin’s scientific research has been inextricably linked with the Steklov Mathematical Institute. He defended his Ph.D. thesis “Spaces close to normal and bicompact extensions” in 1977, and his D.Sc. thesis “The method of inverse spectra in the topology of bicompacta” in 1979.

Shchepin’s mathematical style is characterised by his innovative point of view on well-known objects, leading to completely unexpected results and approaches. Another distinguishing feature is a successful and non-trivial combination of very different areas of activity, both in topology and outside it. People who only know him as an expert in geometric and general topology are often astonished by the depth of his interests in computer science and information technology, in mathematical analysis and pedagogy, as well as in the history of mathematics and philosophy.

Shchepin and his wife Nina Alekseevna have four sons and five grandchildren. The two eldest twin sons, while serving in the army, went through the most difficult periods of the first Chechen campaign.

The early results

While still an undergraduate student, Shchepin obtained several striking results that solved well-known problems in topology:

$\bullet$ A construction of a not uniformly paracompact metric space [3], giving a solution to a problem of A. Stone, better known from a book by J. Isbell. This problem was also independently solved by J. Pelant.^1[x]1J. Pelant, “Cardinal reflections and point-character of uniformities counterexamples”, Seminar uniform spaces (Prague 1973–1974), ed. Z. Frolik, Ceskoslovenska Akademie Ved, Matematicky Ustav., Praha, 1975, 149–158. A simpler solution was found much later by A. Hohti.^2[x]2A. Hohti, “An infinitary version of Sperner’s Lemma”, Comment. Math. Univ. Carolin., 47:3 (2006), 503–514.

$\bullet$ The Minkowski sum of $n$ curves in general position was shown to have dimension at least $n$ [4]. This solved a problem of V. M. Tikhomirov’s. In the case when $n=2$ this was proved by Tikhomirov himself and independently by K. A. Sitnikov in 1965.

$\bullet$ The dimension axiomatics for compact spaces proposed by P. S. Alexandroff was extended to arbitrary metric spaces by replacing the finite sum axiom with the infinite sum axiom. It was shown that the new axiom is indispensable even in the separable case [1]. This provided a full solution to a problem of Alexandroff from 1932 concerning the construction of an axiomatics of dimension theory for the class of separable metric spaces.

$\bullet$ A map from an $n$-sphere to a polyhedron of lower dimension that does not identify antipodes was constructed [2], giving a solution to a problem of L. A. Tumarkin from 1939. An independent solution proposed by M. I. Stesin was also published in the same issue of the journal Doklady Akademii Nauk SSSR ^3[x]3Translated as Doklady: Mathematics.. Although special cases of the Tumarkin problem were stated in books by P. Conner and E. Floyd (1964) and K. Borsuk (1967), it turned out subsequently that the same example as Shchepin’s appeared in a paper of H. Hopf in 1937. On the other hand Shchepin’s work [2] also contained a solution to another question, which was raised in fact in Hopf’s paper, namely, Shchepin showed that any map from a $2n$-dimensional sphere to an $n$-dimensional polyhedron identifies a pair of antipodes. For the further history of this problem see [38] by A. Yu. Volovikov and Schepin.

General topology

In the second half of the 1970s, Shchepin developed the method of inverse spectra for the investigation of non-metrisable compact spaces [5]. This method is based on his famous spectral theorem, establishing the existence of isomorphic subspectra in regular spectra with homeomorphic limit spaces. Shchepin used this method to solve a number of well-known problems stated by A. Pełczyński. In particular, E. V. Shchepin showed that the space $\exp D^\tau$ of closed subsets of the Cantor cube is not homeomorphic to $D^\tau$ for $\tau>\aleph_1$ (although the two spaces are homeomorphic for $\tau=\aleph_1$, as shown by S. M. Sirota^4[x]4S. Sirota, “The spectral representation of spaces of closed subsets of bicompacta” (Russian), Dokl. Akad. Nauk SSSR, 181:5 (1968), 1069–1072.). Moreover, it turned out that the situation with the space of closed sets in typical. Namely, Shchepin showed that for any functor $F$ of exponential type (for example, for the symmetric square functor) the space $F(D^\tau)$ is not homeomorphic to $D^\tau$, whereas $F(D^{\aleph_1})$ can be homeomorphic or not homeomorphic to $D^{\aleph_1}$.

The spectral theorem can be used to approximate non-metrisable compacta with an action of a countable group $\Gamma$ by metric compacta with an action of $\Gamma$. ^5[x]5A. N. Dranishnikov, “Asymptotic topology”, Uspekhi Mat. Nauk, 55:6 (2000), 71–116; English transl. in Russian Math. Surveys, 55:6 (2000), 1085–1129. When applied to the action of the fundamental group of a manifold on the Higson–Roe corona of its universal cover (which is non-metrisable by definition), this fact proved to be extremely useful in the rough-geometry approach to Novikov’s higher signature conjecture.^6[x]6A. Dranishnikov, S. Ferry, S. Weinberger, “Anétale approach to the Novikov conjecture”, Comm. Pure Appl. Math., 61:2 (2008), 139–155.

The fundamental notion of adequacy was also introduced in [5]: a class of spaces $A$ is adequate to a class of maps $B$ if spaces in the class $A$ are characterised by their decomposability into regular spectra with projections belonging to $B$. In [5] three deep theorems on adequacy were proved: the class of kappa-metrisable spaces (introduced in [5]) is adequate to the class of open maps^7[x]7The kappa-metric is an axiomatisation of the distance between points and canonically closed subsets., the class of absolute retracts is adequate to the class of soft maps, and the class of Dugundji spaces (introduced by Pełczyński) is adequate to the class of $0$-soft maps. Soft and $0$-soft maps, also introduced in [5], became subsequently an object of intensive research^8[x]8See, for example, the book: V. V. Fedorchuk and A. I. Chigogidze, Absolute retracts and infinite-dimensional manifolds, Nauka, Moscow 1992. 232 pp. (Russian)..

The adequacy theorem for absolute retracts enabled Shchepin to obtain an unexpected result on the metrisability of finite-dimensional absolute retracts [6] and to prove a theorem, looking improbable at first glance, that every compact homogeneous absolute retract is homeomorphic to the Tychonoff cube $I^{\tau} $ (see [7]). The proof of the latter required the help of H. Toruńczyk and J. West, who, in answering a question of Shchepin, proved a theorem on the triviality of bundles with fibre equal to the Hilbert cube.

The methods in [5] were used in very different areas of topology, for example, in S. P. Gul’ko’s work on function spaces^9[x]9S. P. Gul’ko, “On the properties of some function spaces”, Dokl. Akad. Nauk SSSR, 243:4 (1978), 839–842. or in the adaptation of the spectral method to Boolean algebras which was proposed by L. B. Shapiro^10[x]10See L. Heindorf and L. B. Shapiro, Nearly projective Boolean algebras, Lect. Notes in Math., 1596, Springer-Verlag, Berlin, 1994, x+202 pp..

The work [5] was followed by the paper [8], which completed the development of Shchepin’s spectral method to a certain extent. In [8] the concept of a normal functor was introduced and investigated. It laid the foundation for a new line of research in topology, which has become the subject of dozens of papers. Spectral search, sigma-spectra, the functor of probability measures – all these concepts were introduced in [8] into topological use.

Starting from 1980, the emphasis in Shchepin’s scientific work shifted from general to geometric topology (see, for example, [10] and [11]).

The Hilbert–Smith Conjecture

One of the most important open questions in geometric topology is the Hilbert–Smith conjecture: is a compact group acting effectively on a connected manifold necessarily a Lie group? In the well-known list of open problems in topology^11[x]11R. J. Daverman, “Problems about finite-dimensional manifolds”, Open problems in topology, North-Holland, Amsterdam, 1990, 431–455., it comes immediately after the conjectures of Poincaré and Thurston (now proved by G. Perelman) and before the four-dimensional smooth conjectures of Poincaré and Schoenflies. Back in 1946, S. Bochner and D. Montgomery proved the Hilbert–Smith conjecture for smooth actions. As of today, one of the best results in this direction is Shchepin’s theorem [25] that the Hilbert–Smith conjecture is true for Lipschitz actions. The proof combines various techniques, extending from the homological dimension of the orbit spaces for $p$-adic actions to the Hausdorff dimension^12[x]12This technique also works for Hölder actions: see I. Maleshich, “The Hilbert–Smith conjecture for Hölder actions”, Uspekhi Mat. Nauk, 52:2 (1997), 173–174; English transl. in Russian Math. Surveys, 52:2 (1997), 407–408.. In [30] Shchepin also proposed another approach by proving the Hilbert–Smith conjecture for free, rather than effective, Lipschitz actions of compact groups on spaces of finite Hausdorff volume (this class of spaces is much wider than the Riemannian manifolds). Taking the results of [25] into account, he also proved that the isometry group of a compact manifold is a Lie group in the case when its Hausdorff dimension exceeds its topological dimension by $2$ at most.

Dimension theory

Among Shchepin’s results on dimension theory we note an example (joint with A. N. Dranishnikov [19]) of a two-dimensional subset $W$ of $\mathbb{R}^3$ and a one-dimensional continuum $Y$ such that the product $W\times Y$ is two- dimensional. This amazing example solved the long-standing problems stated by K. Nagami and V. I. Kuz’minov.

The following fundamental result (joint with A. N. Dranishnikov [13]) can be attributed to both dimension theory and embedding theory: the set of embeddings is dense in the space of maps from a compact space $X$ to Euclidean space $\mathbb{R}^n$ if and only if $\dim(X\times X)<n$. The same result was obtained simultaneously and independently by the Polish mathematicians J. Krasinkiewicz and J. Spież. Recall that the inequality $\dim(X\times X)<2\dim X$ holds for Boltyanskii compacta. These results are closely related to a series of works by Shchepin, A. N. Dranishnikov, and D. Repovš, which made a great contribution to the problem of the stability of the intersection of two compacta in Euclidean space [21], [28]. The problem of intersection stability was finally solved by A. N. Dranishnikov and, in codimension $2$, by M. Levin.^13[x]13A. N. Dranishnikov, “On the mapping intersection problem”, Pacific J. Math., 173:2 (1996), 403–412; “On the dimension of the product of two compacta and the dimension of their intersection in general position in Euclidean space”, Trans. Amer. Math. Soc., 352:12 (2000), 5599–5618; and M. Levin, “On the unstable intersection conjecture”, Geom. Topol., 22:5 (2018), 2511–2532.

Shchepin’s arithmetic

Shchepin’s results mentioned in the previous section are essentially based on the homological dimension theory of compact metric spaces, founded by Alexandroff and M. F. Bockstein and developed further by Kuz’minov and Dranishnikov^14[x]14V. I. Kuz’minov, “Homological dimension theory”, Uspekhi Mat. Nauk, 23:5 (1968), 3–49; English transl. in Russian Math. Surveys, 23:5 (1968), 1–45; and A. N. Dranishnikov, “Homological dimension theory”, Uspekhi Mat. Nauk, 43:4 (1988), 11–55, English transl. in Russian Math. Surveys, 43:4 (1988), 11–63.. Shchepin brought ideas from tropical geometry to bear on homological dimension theory and proposed a new arithmetic of dimension [29]. By definition, Shchepin’s natural numbers are the set $\mathbb{N}_{\mathrm{S}}=\mathbb{N}^-\cup\mathbb{N}\cup\mathbb{N}^+\cup\{ 0\}$ consisting of three copies of ordinary natural numbers and zero, with the operations of taking the maximum and addition. The maximum in $\mathbb{N}_{\mathrm{S}}$ is taken with respect to the linear order $0<1^-<1<1^+<2^-<2<2^+<3^-<3<3^+<\cdots$. Addition in $\mathbb{N}_{\mathrm{S}}$ is defined by

Using Bockstein’s theory, for any metric compact space $X$ one can define uniquely its dimension function $D_X\colon\mathcal{P}\to\mathbb{N}_{\mathrm{S}}$, where $\mathcal{P}$ is the set of primes plus zero. In the case of finite-dimensional compacta, the dimension $\dim X$ is equal to the least integer upper bound of the dimension function:

Brouwer’s Conjecture

In 1912 H. Poincaré suggested an inductive definition of the dimension of a topological space. This idea was formalized by L. Brouwer, who defined in 1913 a dimensional invariant $\operatorname{Dg}$ of topological spaces, which he called Dimensionsgrad. Other definitions of dimension appeared subsequently, due to H. Lebesgue, P. S. Urysohn, K. Menger, W. Hurewicz, Alexandroff, and E. Čech. All of them were all proved to be equivalent one to another in the class of metric compact spaces, and by the end of the 1920s they became the commonly accepted definition of dimension (the Lebesgue dimension $\dim$). Brouwer conjectured repeatedly in his works of the 1920s that $\operatorname{Dg}$ also coincides with $\dim$ for metric compact spaces. Only relatively recently has it been proved that he was right: the corresponding theorem was published by Shchepin in collaboration with M. Levin and V. V. Fedorchuk [31].

Embedding compact sets

The Moscow school of geometric topology was greatly influenced by the spectral criterion for embeddability of an $n$-dimensional compact set $X$ in Euclidean space $\mathbb{R}^m$ found by Shchepin and M. A. Shtan’ko [9]. For $m-n\geqslant 3$ they reduced the question of the embeddability of $X$ in $\mathbb{R}^m$ essentially to the existence of a level-preserving embedding in $\mathbb {R}^m\times[0,\infty)$ of the telescope of an inverse sequence of polyhedra approximating $X$. The Shchepin–Shtan’ko criterion has aroused considerable interest in the problems of approximation by embeddings and isotopic realization of a given map from a polyhedron to $\mathbb{R}^m$. For a long period of time they became one of the central topics at Shchepin’s seminar in the Steklov Mathematical Institute (see works of 1996–2004 by P. M. Akhmetiev, S. A. Melikhov, A. B. Skopenkov, and M. B. Skopenkov). In the joint work of Shchepin and Melikhov [39] the Shchepin–Shtan’sko criterion was used to obtain a homotopy-theoretic criterion for embeddability of $X$ in $\mathbb{R}^m$ in the metastable rank ($2m>3n+3$) and to prove the completeness of the van Kampen obstruction to the embeddability of $X$ in $\mathbb{R}^{2n}$ ($n>3$). This led, in particular, to several unexpected geometric theorems, which were proved algebraically (by using the functor $\lim^1$ and investigating the commutation of the direct and inverse limits of Abelian groups).

The realization of Steenrod cycles

Shchepin made two fundamental contributions to the homology theory of compact spaces: a theorem on the equivalence of homological local $n$-connectedness in the sense of Čech and Steenrod homology, and a theorem on the realization of Steenrod cycles of a homologically locally $n$-connected compact space by fractal pseudomanifolds. In the one-dimensional case both theorems were published in the joint paper [17] with W. Mitchell and Repovš. The equivalence theorem was presented by Shchepin at the International Congress of Mathematicians in Kyoto (1990). In the general case the proofs of these two theorems of Shchepin’s were first published in Melikhov’s paper^16[x]16S. A. Melikhov, “Steenrod homotopy”, Uspekhi Mat. Nauk, 64:3 (2009), 73–166; English transl. in Russian Math. Surveys, 64:3 (2009), 469–551..

Selections and convexity

Shchepin used Milyutin maps and selections in measure spaces in a non-trivial way to derive Michael’s convex-valued selection theorem from its zero-dimensional case [18]. Continuous selections were the subject of a series of joint works by Shchepin with P. V. Semenov and Repovš [32], [20], [26]. In a joint work with N. B. Brodsky [22] he proved a filtration theorem on selection, which improved Michael’s finite-dimensional theorem. In [27], [40], [43] the ‘filtration’ approach was used to construct sections of Serre fibrations whose fibres are manifolds of dimension $2$ or $3$.

Back in his student years, Shchepin dealt with problems of the convexity of Chebyshev sets. Subsequently, they led him to do research on ‘topological tomography’, the problem of characterising the convexity of a body in terms of the topological properties of its hyperplane sections, in the spirit of R. Aumann’s theorem. This problem was the subject of two joint papers with L. Montejano. In the first paper [23] they proved that the acyclicity of the cross-sections of a finite-dimensional acyclic body by supporting hyperplanes implies its convexity. In the second paper [34] the infinite-dimensional version of Aumann’s theorem was established.

Mathematical analysis

With the beginning of the new century, Shchepin’s mathematical interests shifted gradually from topology to analysis. Many years of teaching had led him to develop a very unusual course of analysis (see [48]). The lecture on divergent series in his course [33] presented a generalization of the Euler summation method for divergent numerical series to function series.

Of considerable interest are Shchepin’s works on developing further Leibniz’ intuitive ideas about the essence of the differential, giving them a rigorous form in the sense of Cauchy, and further constructions of an integral in the spirit of Perron and Stieltjes [49], as well as the relationship of these concepts with non-standard analysis [53].

In his important work [50] he introduced the concept of a greedy sum for unordered numeric and matrix arrays. Using the theory of generalized Dirichlet series he proved a multiplicativity theorem for greedy sums, which is an analogue of Abel’s theorem for products of series.

Fractal geometry

In 1958, L. V. Keldysh constructed a dimension-increasing map from a three-dimensional cube^17[x]17L. V. Keldysh, “An open map from a three-dimensional cube to four-dimensional cube”, Mat. Prosveshchenie, Ser. 2, no. 3 (1958), 259–264 (Russian).. In 1987 Shchepin, following an idea of A. V. Chernavskii, explored the possibilities of using this map in coding problems for continuous information transmission, stating the so-called ‘principle of three channels’ [12]. Subsequently, in [37] he began a systematic study of fractal Peano curves. In a series of joint works with K. E. Bauman [41], A. A. Korneev [51] and Yu. V. Malykhin [52] they developed a theory and algorithms for finding curves with minimal stretching, which are important in applications.

There is also a related interesting problem of V. I. Arnold on the existence of a map from a square onto a cube with Hölder exponent $2/3$. Here Shchepin was successful, on the one hand, in obtaining a negative result, proving the impossibility of a fractal map of a square onto a cube [44], and on the other hand, in constructing, with the computer help of his son Nikita, a combinatorially continuous map of a $64$-pixel square onto a $64$-pixel cube [36].

Computer science

Perhaps the most cited here is the series of joint papers with N. Vakhania on scheduling theory for multiprocessor systems (see [35], [42], [45], and the references there). The monograph Information, coding and prediction written with N. K. Vereshchagin [46] summed up Shchepin’s teaching experience at Yandex.

In the late 1980s Shchepin organised a seminar on pattern recognition at the Steklov Institute. Among the active participants of this seminar were G. M. Nepomnyashchiy, Yu. A. Burov, and A. A. Burov. E. V. Shchepin was the scientific director of the project on programming systems for monitoring dynamical sets. V. M. Kliatskine was the project manager, and V. V. Mottl and N. V. Petri took part in the project. During the implementation of this project, Shchepin developed original algorithms for the linear description of point sets. The scientific results of the project were published in [14] and [15].

Subsequently, a group of researchers from this project, together with N. V. Kotovich, formed the core of the Scriptum software company, which launched the Crypt OCR system on the market. This recognition system was based on the topological ‘PRS code’ developed by Shchepin [47]. In addition to optical character recognition, principles of which are outlined in the joint article [16] by Schepin and Nepomnyashchiy, the system included powerful algorithms for text structure analysis. The Crypt system coped successfully not only with modern texts, but also, for example, with the recognition of complex Norwegian tabular forms from the 19th century. (See the joint work [24] and the references there).

The seminar on geometric topology

In 1980 Shchepin and Shtan’ko organised a seminar on geometric topology in the Steklov Institute, which continued the traditions of the seminar of Lyudmila Vsevolodovna Keldysh and attracted many of its former participants^18[x]18For the seminar of Keldysh, see A. V. Chernavskii, “On the work of L. V. Keldysh and her seminar”, Uspekhi Mat. Nauk, 60:4 (2005), 11–36; English transl. in Russian Math. Surveys, 60:4 (2005), 589–614.. At the initial stage, the regular participants of the seminar included Shchepin with his students Dranishnikov and M. V. Smurov, and also Chernavskii and Shtan’ko. In the 1980s S. Matveev, M. Farber, A. Chigogidze, P. Semenov, L. Shapiro, A. Skopenkov, V. Pidstrigach, L. Zerkalov, and M. Zarichny joined the seminar. Among the new participants in the 1990s were P. Akhmetiev, N. Brodsky, A. Volovikov, A. Karinsky, S. Melikhov, R. Mikhailov, R. Sadykov, K. Salikhov, and Yu. Turygin. In the 21st century new active participants joined, including M. Skopenkov, E. Kudryavtseva, O. Frolkina, A. Lightfoot, A. Dunaikin, M. Tyomkin, A. Ryabichev, D. Tereshkin, A. Gorelov, and the list of them continues to grow.

For a long time Shchepin was the head of various grant projects and supported the cooperation of Russian topologists with colleagues from other countries, in particular, Slovenia and Mexico. At the time of an almost total lack of money for Russian science, this contributed greatly to the survival of the academic school.

Shchepin devotes a lot of time and energy to pedagogical work. For many years he worked in his native Kolmogorov boarding school and also lectured in the Moscow State Pedagogical University. He made a significant contribution to the development of the teaching system at the Yandex School of Data Analysis. Among the students of Shchepin are A. N. Dranishnikov (University of Florida), A. B. Skopenkov (School of Applied Mathematics and Informatics MIPT), N. B. Brodsky (University of Tennessee), S. A. Melikhov (Steklov Mathematical Institute), M. V. Smurov, V. M. Kliatskine, K. E. Bauman, A. A. Korneev, A. R. Salomasov (director of Moscow school no. 1522), V. Stakhovsky, G. Turkanov, V. Tokarev.

We wish Evgeny Vitalievich good health and further scientific and pedagogical achievements.

List of cited papers of E. V. Schepin
1.	E. V. Ščepin, “Axiomatics of the dimension of metric spaces”, Mat. Sb., 92(134):1(9) (1973), 135–141      ; English transl. in Sb. Math., 21:1 (1973), 137–143
2.	E. V. Ščepin, “On a problem of L. A. Tumarkin”, Dokl. Akaf. Nauk SSSR, 217:1 (1974), 42–43      ; English transl. in Soviet Math. Dokl., 15:4 (1974), 1024–1026
3.	E. V. Ščepin, “On a problem of Isbell”, Dokl. Akad. Nauk SSSR, 222:3 (1975), 541–543      ; English tranasl. in Soviet Math. Dokl., 16:3 (1975), 685–687
4.	E. V. Shchepin, “The dimension of a sum of curves”, Uspekhi Mat. Nauk, 30:4(184) (1975), 267–268 (Russian)
5.	E. V. Shchepin, “Topology of limit spaces of uncountable inverse spectra”, Uspekhi Mat. Nauk, 31:5(191) (1976), 191–226      ; English transl. in Russian Math. Surveys, 31:5 (1976), 155–191
6.	E. V. Shchepin, “Topology of limit spaces of uncountable inverse spectra”, Dokl. Akad. Nauk SSSR, 233:3 (1977), 304–307      ; English trabsl. in xjour Soviet Math. Dokl. 18:2 (1977), 402–406
7.	E. V. Shchepin, “On Tychonoff manifolds”, Dokl. Akad. Nauk SSSR, 246:3 (1979), 551–554      ; English transl. in Soviet Math. Dokl., 20:3 (1979), 511–515
8.	E. V. Shchepin, “Functors and uncountable powers of compacta”, Uspekhi Mat. Nauk, 36:3(219) (1981), 3–62      ; English transl. in Russian Math. Surveys, 36:3 (1981), 1–71
9.	M. A. Shtan'lo and E. V. Shchepin, “A spectral criterion for the embeddavility of a compact set in a Euclidean space”, Proceeding of the Leningrad International Mathematical Conference, Nauka, Leningrad, 1983, 135–142 (Russian)
10.	E. V. Shchepin, “Soft maps of manifolds”, Uspekhi Mat. Nauk, 39:5(239) (1984), 209–224      ; English transl. in Russian Math. Surveys, 39:5 (1984), 251–270
11.	A. N. Dranishnikov and E. V. Schepin, “Cell-like maps. The problem of raising dimension”, Uspekhi Mat. Nauk, 41:6(252) (1986), 49–90      ; English transl. in Russian Math. Surveys, 41:6 (1986), 59–111
12.	E. V Shchepin, “Dimension-raising maps and contiuous information transmission”, Questions in pure and applied mathematics, v. 1, Priokskoe Knizhnoe Izdatel'stvo, Tula, 1987, 148–155 (Russian)
13.	A. N. Dranišnikov, D. Repovš, and E. V. Ščepin, “On intersections of compacta of complementary dimensions in Euclidean space”, Topology Appl., 38:3 (1991), 237–253
14.	V. M. Klyatskin (Kliatskine), V. V. Mottl, and E. V. Schepin, “A probabilistic approach to the problem of skeletonizing point images”, Pattern Recognit. Image Anal., 1:4 (1991), 430–439
15.	V. M. Buchstaber, V. M. Klyatskin (Kliatskine), V. V. Mottl', and E. V. Shchepin, “An automatic system for an analysis of planar point images by means of skeletonization as a tool for solving problems in applied statistics”, Programmnye Produkty i Sistemy, 3 (1991), 52–62 (Russian)
16.	E. V. Shchepin and G. M. Nepomnyashchiy, “Character recognition via critical points”, Int. J. Imaging Syst. Technol., 3:3 (1991), 213–221
17.	W. J. R. Mitchell, D. Repovš, and E. V. Ščepin, “On 1-cycles and the finite dimensionality of homology 4-manifolds”, Topology, 31:3 (1992), 605–623
18.	P. V. Semenov and E. V. Shchepin, “Universality of the zero-dimensional selection theorem”, Funktsional. Anal. i Prilozhen., 26:2 (1992), 36–40      ; English transl. in Funct. Anal. Appl., 26:2 (1992), 105–108
19.	A. N. Dranishnikov, D. Repovš, and E. V. Ščepin, “Dimension of products with continua”, Topology Proc., 18 (1993), 57–73
20.	D. Repovš, P. V. Semenov, and E. V. Ščepin, “On zero-dimensional Milutin maps and Michael selection theorems”, Topology Appl., 54:1-3 (1993), 77–83
21.	A. N. Dranišnikov, D. Repovš, and E. V. Ščepin, “On approximation and embedding problems for cohomological dimension”, Topology Appl., 55:1 (1994), 67–86
22.	E. V. Shchepin and N. B. Brodskii (Brodsky), “Selections of filtered multivalued mappings”, Maps and Dimension, Tr. Mat. Inst. Steklov., 212, Nauka, Moscow, 1996, 220–240      ; English transl. in Proc. Steklov Inst. Math., 212 (1996), 209–229
23.	L. Montejano and E. V. Shchepin, “A characterization of convex sets in terms of acyclic support sets”, Bull. London Math. Soc., 28:5 (1996), 501–504
24.	V. Kliatskine, E. Shchepin, G. Thorvaldsen, K. Zingerman, and V. Lazarev, “A structured method for the recognition of complex historical tables”, History and Computing, 9:1-3 (1997), 58–77
25.	D. Repovš and E. V. Ščepin, “A proof of the Hilbert–Smith conjecture for actions by Lipschitz maps”, Math. Ann., 308:2 (1997), 361–364
26.	D. Repovš, P. V. Semenov, and E. V. Ščepin, “On exact Milyutin mappings”, Topology Appl., 81:3 (1997), 197–205
27.	N. B. Brodskij (Brodsky) and E. V. Shchepin, “Poincaré duality and Serre fibrations”, Topology Appl., 80:1-2 (1997), 55–61
28.	A. N. Dranishnikov, D. Repovš, and E. V. Ščepin, “Transversal intersection formula for compacta”, Topology Appl., 85:1-3 (1998), 93–117
29.	E. V. Shchepin, “Arithmetic of dimension theory”, Uspekhi Mat. Nauk, 53:5(323) (1998), 115–212        ; English transl. in Russian Math. Surveys, 53:5 (1998), 975–1069
30.	E. V. Shchepin, “Hausdorff dimension and the dynamics of diffeomorphisms”, Mat. Zametki, 65:3 (1999), 457–463        ; English transl. in Math. Notes, 65:3 (1999), 381–385
31.	E. V. Shchepin, “Hausdorff dimension and the dynamics of diffeomorphisms”, Uspekhi Mat. Nauk, 54:2(326) (1999), 193–194        ; English transl. in xjour Russian Math. Surveys 54:2 (1999), 432–433
32.	P. V. Semenov and E. V. Shchepin, “Selection approach to multivalued separation theorems”, Topol. Methods Nonlinear Anal., 14:1 (1999), 183–192
33.	E. V. Shchepin, Uppsala lectures on calculus, 2003, viii+129 pp. http://at.yorku.ca/i/a/a/z/20.htm
34.	L. Montejano and E. Shchepin, “Topological tomography in convexity”, Bull. London Math. Soc., 34:3 (2002), 353–358
35.	N. Vakhania and E. Shchepin, “Concurrent operations can be parallelized in scheduling multiprocessor job shop”, J. Sched., 5:3 (2002), 227–245
36.	E. V. Shchepin, M. V. Shevelev, and N. E. Schepin, “On the topology of the number 64”, Chebyshevskii Sb., 4:4 (2003), 153–172 (Russian)
37.	E. V. Shchepin, “On fractal Peano curves”, Geometric topology and set theory, Tr. Mat. Inst. Steklov., 247, Nauka, MAIK ‘Nauka/Interperiodika’, Moscow, 2004, 294–303      ; English transl. in Proc. Steklov Inst. Math., 247 (2004), 272–280
38.	A. Yu. Volovikov and E. V. Shchepin, “Antipodes and embeddings”, Mat. Sb., 196:1 (2005), 3–32        ; English transl. in Sb. Math., 196:1 (2005), 1–28
39.	S. A. Melikhov and E. V. Shchepin, The telescope approach to embeddability of compacta, 2006, 26 pp., arXiv: 0612085
40.	N. Brodsky, A. Chigogidze, and E. V. Ščepin, “Sections of Serre fibrations with 2-manifold fibers”, Topology Appl., 155:8 (2008), 773–782
41.	E. V. Shchepin and K. E. Bauman, “Minimal Peano curve”, Geometry, topology, and mathematical physics. 3, Tr. Mat. Inst. Steklov., 263, MAIK ‘Nauka/Interperiodika’, Moscow, 2008, 251–271      ; English transl. in Proc. Steklov Inst. Math., 263 (2008), 236–256
42.	E. V. Shchepin and N. Vakhania, “On the geometry, preemptions and complexity of multiprocessor and shop scheduling”, Ann. Oper. Res., 159 (2008), 183–213
43.	N. Brodskiy (Brodsky), A. Chigogidze, and E. V. Shchepin, “Local sections of Serre fibrations with 3-manifold fibers”, Topology Appl., 157:4 (2010), 809–814
44.	E. V. Shchepin, “On Hölder maps of cubes”, Math. Notes, 87:5-6 (2010), 757–767
45.	E. V. Shchepin and N. Vakhania, “A note on the proof of the complexity of the little-preemptive open-shop problem”, Ann. Oper. Res., 191 (2011), 251–253
46.	N. K. Vereshchagin and E. V. Shchepin, Information, coding, and predicting, Moscow Center for Continuous Mathematical Education, Moscow, 2012, 236 pp. (Russian)
47.	E. V. Shchepin, “Crossing code”, Uspekhi Mat. Nauk, 68:6(414) (2013), 177–178        ; English transl. in Russian Math. Surveys, 68:6 (2013), 1142–1144
48.	E. V. Shchepin, “In search of lost analysis”, Mathematics and reality, Faculty of Phylosophy, Moscow State University, Moscow, 2014, 496–504 (Russian)
49.	E. V. Shchepin, “The Leibniz differential and the Perron–Stieltjes integral”, Fundam. Prikl. Mat., 20:6 (2015), 237–258      ; English transl. in J. Math. Sci. (N.Y.), 233:1 (2018), 157–171
50.	E. V. Shchepin, “Summation of unordered arrays”, Funktsional. Anal. Prilozhen., 52:1 (2018), 43–55        ; English transl. in Funct. Anal. Appl., 52:1 (2018), 35–44
51.	A. A. Korneev and E. V. Shchepin, “$L_\infty$-locality of three-dimensional Peano curves”, Topology and physics, Tr. Mat. Inst. Steklov., 302, MAIK ‘Nauka/Interperiodika’, Moscow, 2018, 234–267        ; English transl. in Proc. Steklov Inst. Math., 302 (2018), 217–249
52.	Yu. V. Malykhin and E. V. Shchepin, “Minimal self-similar Peano curve of genus $5\times 5$”, Dokl. Ross. Akad. Nauk Mat. Inform. Prots. Upravl., 491 (2020), 68–72      ; English transl. in Dokl. Math., 101:2 (2020), 135–138
53.	E. V. Shchepin, Leibniz differential and non-stantard calculus, 2020, 7 pp., arXiv: 2002.12451

Citation in format AMSBIB

\Bibitem{BusBucDra22}
\by V.~I.~Buslaev, V.~M.~Buchstaber, A.~N.~Dranishnikov, V.~M.~Kliatskine, S.~A.~Melikhov, L.~Montejano, S.~P.~Novikov, P.~V.~Semenov
\paper Evgenii Vital'evich Shchepin (on his 70th birthday)
\jour Russian Math. Surveys
\yr 2022
\vol 77
\issue 3
\pages 559--569
\mathnet{http://mi.mathnet.ru//eng/rm10043}
\crossref{https://doi.org/10.1070/RM10043}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461383}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022RuMaS..77..559B}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000992284200009}


This publication is cited in the following 1 articles: