Note on Bessaga-Klee classification

Marek Cúth, and Ondřej F. K. Kalenda. "Note on Bessaga-Klee classification." Colloquium Mathematicae 140.1 (2015): 59-74. <http://eudml.org/doc/286188>.

@article{MarekCúth2015,
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 also works in the topological case.},
author = {Marek Cúth, Ondřej F. K. Kalenda},
journal = {Colloquium Mathematicae},
keywords = {closed convex body; homeomorphism of pairs; Bessaga-Klee classification; characteristic cone},
language = {eng},
number = {1},
pages = {59-74},
title = {Note on Bessaga-Klee classification},
url = {http://eudml.org/doc/286188},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Marek Cúth
AU - Ondřej F. K. Kalenda
TI - Note on Bessaga-Klee classification
JO - Colloquium Mathematicae
PY - 2015
VL - 140
IS - 1
SP - 59
EP - 74
AB - 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.
LA - eng
KW - closed convex body; homeomorphism of pairs; Bessaga-Klee classification; characteristic cone
UR - http://eudml.org/doc/286188
ER -