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Matematicheskie Zametki, 2008, Volume 84, Issue 4, Pages 527–531
DOI: https://doi.org/10.4213/mzm6136 (Mi mzm6136) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Nonincrease of Density and Weak Density under Weakly Normal Functors

R. B. Beshimov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
Full-text PDF (413 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm6136
Abstract: In this paper, it is proved that if a covariant functor $\mathscr F\colon\mathrm{Comp}\to\mathrm{Comp}$ is weakly normal, then $d(\mathscr F^\beta(X))\le d(X)$ and $wd(\mathscr F^\beta(X))\le wd(X)$ for any infinite Tychonoff space $X$.
Keywords: normal functor, weakly normal functor, density, weak density, Hausdorff space, cellularity of a space, Tychonoff space, Stone–Čech compactification.
Received: 04.05.2007
Revised: 21.12.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 4, Pages 493–497
DOI: https://doi.org/10.1134/S0001434608090216
Bibliographic databases:
UDC: 515.17
Language: Russian
Citation: R. B. Beshimov, “Nonincrease of Density and Weak Density under Weakly Normal Functors”, Mat. Zametki, 84:4 (2008), 527–531; Math. Notes, 84:4 (2008), 493–497
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm6136
  • https://www.mathnet.ru/eng/mzm/v84/i4/p527
    • This publication is cited in the following 9 articles:
    1. R.B. Beshimov, N.K. Mamadaliev, R.M. Juraev, “On some properties of the space of τ-continuous mappings”, Topology and its Applications, 2025, 109241  crossref
    2. Sh. A. Ayupov, N. K. Mamadaliev, “On Tightness-Type Properties of the Space of Weakly Additive Functionals”, Proc. Steklov Inst. Math., 324 (2024), 18–32  mathnet  crossref  crossref  mathscinet  zmath
    3. R.B. Beshimov, N.K. Mamadaliev, “On functional tightness and local density of the space of probability measures”, Topology and its Applications, 329 (2023), 108364  crossref
    4. Beshimov R.B., Georgiou D.N., Mamadaliev N.K., “On Tau-Bounded Spaces and Hyperspaces”, Filomat, 36:1 (2022), 187–193  crossref  mathscinet  isi
    5. Ljubisa Kocinac, Farkhod Mukhamadiev, Anvar Sadullaev, “Some topological and cardinal properties of the space of permutation degree”, Filomat, 36:20 (2022), 7059  crossref
    6. T. K. Yuldashev, F. G. Mukhamadiev, “Some Topological Properties of the Space of Probability Measures”, Lobachevskii J Math, 43:11 (2022), 3310  crossref
    7. Beshimov R.B., Georgiou D.N., Zhuraev R.M., “Index Boundedness and Uniform Connectedness of Space of the G-Permutation Degree”, Appl. Gen. Topol., 22:2 (2021), 447–459  crossref  mathscinet  isi
    8. Beshimov R.B., Safarova D.T., “Some Topological Properties of a Functor of Finite Degree”, Lobachevskii J. Math., 42:12 (2021), 2744–2753  crossref  mathscinet  isi
    9. Beshimov R.B., Mamadaliev N.K., “On the functor of semiadditive ? -smooth functionals”, Topology Appl., 221 (2017), 167–177  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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