The research explores piecewise approximatively compact Chebyshev sets in Banach spaces, highlighting their unique properties.
We consider approximation by piecewise approximatively compact Chebyshev sets in linear normed spaces. We show that, in locally uniformly convex Banach spaces, such sets are suns and are B -path-connected.
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I. G. Tsar’kov (2026) studied this question.
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