Note on Bessaga–Klee classification

Marek Cúth¹ ; Ondřej F. K. Kalenda¹

¹ Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 18675 Praha 8, Czech Republic

Colloquium Mathematicum, Tome 140 (2015) no. 1, pp. 59-74

Résumé

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 also works in the topological case.

Détail

DOI : 10.4064/cm140-1-5

Keywords: collect several variants proof third bessaga klee relative classification closed convex bodies topological vector spaces motivated have found anywhere literature complete correct proof particular point out error proof given book nbsp bessaga nbsp czy ski further provide simplified version nbsp dobrowolskis proof smooth classification smooth convex bodies banach spaces which works topological