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On approximative properties of locally Chebyshev sets. (English) Zbl 1405.41017
Summary: A locally Chebyshev set is a set whose intersection with some closed neighbourhood with center at any point of this set is a Chebyshev set. The paper is concerned with local and global approximative properties of sets. A number of new properties of locally Chebyshev sets and local strict suns are put forward. We give an elementary proof of the recent Flerov’s result to the effect that in a two-dimensional normed linear space a connected locally Chebyshev set is a Chebyshev set.

41A50 Best approximation, Chebyshev systems