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Admissibility, the locally convex approximation property, and the $ {\rm AR}$-property in linear metric spaces


Author: Nguyen To Nhu
Journal: Proc. Amer. Math. Soc. 123 (1995), 3233-3241
MSC: Primary 54C55; Secondary 54D45
DOI: https://doi.org/10.1090/S0002-9939-1995-1246533-8
MathSciNet review: 1246533
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Abstract: We introduce the notion of the locally convex approximation property (the LCAP) for convex sets in linear metric spaces. The LCAP is an extension of the notion of admissibility of Klee. We prove that any convex set with the LCAP is an AR.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1246533-8
Keywords: Linear metric spaces, convex sets, AR-spaces, admissible convex sets, the locally convex approximation property
Article copyright: © Copyright 1995 American Mathematical Society

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