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Antiproximinal sets in the Banach space $$c( X)$$. (English) Zbl 0887.41029
The author proves the existence of antiproximinal convex cell in the Banach space $$c(X)$$ of all $$X$$-valued convergence sequences, where $$X$$ is a non-trivial Banach space (i.e. the existence a nonvoid bounded closed convex body $$V$$ such that no point in $$c(X)\setminus V$$ has a nearest point in $$V$$). The case of the space $$c_0(X)$$ was considered in the author’s earlier paper [Mat. Zametki 17, 449-457 (1975; Zbl 0327.41030)].
Reviewer: K.Najzar (Praha)

##### MSC:
 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A50 Best approximation, Chebyshev systems 46B99 Normed linear spaces and Banach spaces; Banach lattices
##### Keywords:
antiproximinal sets; best approximation
Zbl 0327.41030
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