## 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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