A connected compact locally Chebyshev set in a finite-dimensional space is a Chebyshev set
Konstantin Sergeevich Shklyaev · Sbornik Mathematics · 2019
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.