Bounded Contractibility of Strict Suns in Three-Dimensional Spaces
| Autor: | Alexey Rostislavovich Alimov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Applied Mathematics General Mathematics 010102 general mathematics Dimension (graph theory) Multiplicative function Regular polygon Space (mathematics) 01 natural sciences Contractible space 010305 fluids & plasmas Combinatorics Retract Bounded function 0103 physical sciences 0101 mathematics Normed vector space Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 250:385-390 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-020-05021-7 |
| Popis: | A strict sun in a finite-dimensional (asymmetric) normed space X, dim X ≤ 3, is shown to be P-contractible, P-solar, $$ \overset{{}^{\circ}}{B} $$ -infinitely connected, $$ \overset{{}^{\circ}}{B} $$ -contractible, $$ \overset{{}^{\circ}}{B} $$ -retract, and having a continuous additive (multiplicative) e-selection for any e > 0. A P-acyclic subset of a three-dimensional space is shown to have a continuous e-selection for any e > 0. For the dimension 3, the well-known Tsar’kov characterization of spaces, in which any bounded Chebyshev set is convex, is extended to the case of strict suns. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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