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This article is cited in 1 scientific paper (total in 1 paper)
Imbedding of zero-dimensional compacta in $E^3$
E. V. Sandrakova
Abstract:
In this paper, for an arbitrary zero-dimensional compactum $P$ in $E^3$, a pseudoisotopy $F_t$ of the space $E^3$ onto itself is constructed, taking
a tame zero-dimensional compactum $C$ into $P$; here each nondegenerate preimage of a point under the mapping $F_1$ is a tame arc.
For the zero-dimensional Antoine compactum $A$ a pseudoisotopy $F_t$ of $E^3$ onto itself is constructed taking a tame zero-dimensional compactum into it so that the mapping $F_1$ has a countable set of nondegenerate primages of points, but each of these is not a locally connected continuum.
Bibliography: 11 titles.
Received: 14.05.1970
Citation:
E. V. Sandrakova, “Imbedding of zero-dimensional compacta in $E^3$”, Mat. Sb. (N.S.), 85(127):1(5) (1971), 98–114; Math. USSR-Sb., 14:1 (1971), 99–114
Linking options:
https://www.mathnet.ru/eng/sm3186https://doi.org/10.1070/SM1971v014n01ABEH002606 https://www.mathnet.ru/eng/sm/v127/i1/p98
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Abstract page: | 264 | Russian version PDF: | 81 | English version PDF: | 3 | References: | 36 |
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