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Mat. Zametki, 1997, Volume 62, Issue 6, Pages 803–812 (Mi mz1669)  

This article is cited in 1 scientific paper (total in 1 paper)

Obstructions to the extension of partial maps

S. M. Ageeva, S. A. Bogatyib

a A. S. Pushkin Brest State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: One of the most important problems in topology is the minimization (in some sense) of obstructions to extending a partial map $Z\hookleftarrow A\overset{f}{\to} X$, i.e., of a subset $F\subset Z\setminus A$ such that $f$ can be globally extended to its complement. It is shown that if $Z$ is a fixed metric space with $\dim Z\le n$ and $p,q\ge-1$ are fixed numbers, then obstructions to extending all partial maps $Z\hookleftarrow A\overset{f}{\to} X\in\operatorname{LC}^p\cap \operatorname{C}^q$ can be concentrated in preselected fairly thin subsets of $Z$.

DOI: https://doi.org/10.4213/mzm1669

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English version:
Mathematical Notes, 1997, 62:6, 675–682

Bibliographic databases:

UDC: 515.1
Received: 16.02.1995
Revised: 22.08.1997

Citation: S. M. Ageev, S. A. Bogatyi, “Obstructions to the extension of partial maps”, Mat. Zametki, 62:6 (1997), 803–812; Math. Notes, 62:6 (1997), 675–682

Citation in format AMSBIB
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\paper Obstructions to the extension of partial maps
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\pages 803--812
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\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 6
\pages 675--682
\crossref{https://doi.org/10.1007/BF02355454}
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    This publication is cited in the following articles:
    1. V. V. Fedorchuk, “On some problems of topological dimension theory”, Russian Math. Surveys, 57:2 (2002), 361–398  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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