A connected compact locally Chebyshev set in a finite-dimensional space is a Chebyshev set
-
Published:2020-03-01
Issue:3
Volume:211
Page:455-465
-
ISSN:1064-5616
-
Container-title:Sbornik: Mathematics
-
language:
-
Short-container-title:Sb. Math.
Abstract
Abstract
Let
be a Banach space. A set
is a Chebyshev set if, for each
, there exists a unique best approximation to
in
. A set
is locally Chebyshev if, for any point
, there exists a Chebyshev set
such that some neighbourhood of
in
lies in
. It is shown that each connected compact locally Chebyshev set in a finite-dimensional normed space is a Chebyshev set.
Bibliography: 11 titles.
Funder
Russian Foundation for Basic Research
Ministry of Education and Science of the Russian Federation
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS
Subject
Algebra and Number Theory
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On Locally Chebyshev Sets;Mathematical Notes;2024-04