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Fundam. Prikl. Mat., 2018, Volume 22, Issue 1, Pages 3–11 (Mi fpm1778)  

Bounded contractibility of strict suns in three-dimensional spaces

A. R. Alimovab

a Lomonosov Moscow State University
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A strict sun in a finite-dimensional (asymmetric) normed space $X$, $\operatorname {dim}X \le 3$, is shown to be $P$-contractible, $P$-solar, $\mathring B $-infinitely connected, $\mathring B $-contractible, $\mathring B $-retract, and having a continuous additive (multiplicative) $\varepsilon$-selection for any $\varepsilon > 0$. A $P$-acyclic subset of a three-dimensional space is shown to have a continuous $\varepsilon$-selection for any $\varepsilon > 0$. For the dimension $3$ the well-known Tsar'kov's characterization of spaces, in which any bounded Chebyshev set is convex, is extended to the case of strict suns.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-000333
Ministry of Education and Science of the Russian Federation НШ 6222.2018.1


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Document Type: Article
UDC: 517.982.256+517.982.252

Citation: A. R. Alimov, “Bounded contractibility of strict suns in three-dimensional spaces”, Fundam. Prikl. Mat., 22:1 (2018), 3–11

Citation in format AMSBIB
\Bibitem{Ali18}
\by A.~R.~Alimov
\paper Bounded contractibility of strict suns in three-dimensional spaces
\jour Fundam. Prikl. Mat.
\yr 2018
\vol 22
\issue 1
\pages 3--11
\mathnet{http://mi.mathnet.ru/fpm1778}


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