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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On supportless convex sets in incomplete normed spaces


Author: V. P. Fonf
Journal: Proc. Amer. Math. Soc. 120 (1994), 1173-1176
MSC: Primary 46B20; Secondary 52A05
DOI: https://doi.org/10.1090/S0002-9939-1994-1216811-6
MathSciNet review: 1216811
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Abstract: It is proved that every incomplete separable normed space $ M$ contains a closed bounded convex set $ W$ such that the closed linear span of $ W$ coincides with $ M$ and $ W$ contains no weakly supported points. This theorem answers a question of Klee and a question of Borwein and Tingley.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1216811-6
Article copyright: © Copyright 1994 American Mathematical Society