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.
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