PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Note on Bessaga–Klee classification

Volume 140 / 2015

Marek Cúth, Ondřej F. K. Kalenda Colloquium Mathematicum 140 (2015), 59-74 MSC: Primary 52A07. DOI: 10.4064/cm140-1-5

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.

Authors

  • Marek CúthDepartment of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    18675 Praha 8, Czech Republic
    e-mail
  • Ondřej F. K. KalendaDepartment of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    18675 Praha 8, Czech Republic
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image