Infinite-dimensional polyhedrality

Vladimir P. Fonf, Libor Veselý

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

This paper deals with generalizations of the notion of a polytope to infinite dimensions. The most general definition is the following: a bounded closed convex subset of a Banach space is called a polytope if each of its finite-dimensional affine sections is a (standard) polytope. We study the relationships between eight known definitions of infinite-dimensional polyhedrality. We provide a complete isometric classification of them, which gives solutions to several open problems. An almost complete isomorphic classification is given as well (only one implication remains open).

Original languageEnglish
Pages (from-to)472-494
Number of pages23
JournalCanadian Journal of Mathematics
Volume56
Issue number3
DOIs
StatePublished - 1 Jan 2004

ASJC Scopus subject areas

  • General Mathematics

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