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On \(\sigma\)-Chebyshev subspaces of Banach spaces. (English) Zbl 1004.46016

A subspace \(X_0\) of a Banach space \(X\) is \(\sigma\)-Chebyshev if the projection set of an arbitrary \(x\in X\) is nonempty and \(\sigma\)-compact. A subspace \(X_0\) of a Banach space \(X\) is quasi-Chebyshev if the projection set of an arbitrary \(x\in X\) is nonempty and compact. The authors exhibit an example of a not quasi-Chebychev but \(\sigma\)-Chebychev proximinal subspace.

MSC:

46B25 Classical Banach spaces in the general theory
46A20 Duality theory for topological vector spaces
46A25 Reflexivity and semi-reflexivity
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