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arXiv · 1307.8246

Note on Bessaga-Klee classification

Marek Cúth·Ondřej F. K. Kalenda
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Abstract

We collect several variants of the proof of the third case of the Bessaga-Klee relative classification of closed convex bodies in topological vector spaces. We were motivated by the fact that we have not found anywhere in the literature a complete correct proof. In particular, we point out an error in the proof given in the book of C.~Bessaga and A.~Pełczyński (1975). We further provide a simplified version of T.~Dobrowolski's proof of the smooth classification of smooth convex bodies in Banach spaces which works simultaneously in the topological case.

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Marek Cúth, Ondřej F. K. Kalenda. 2014-11-06. Note on Bessaga-Klee classification. https://doi.org/10.4064/cm140-1-5

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