Infinite-dimensional polyhedrality

Vladimir P. Fonf; Libor Veselý

doi:10.4153/CJM-2004-022-7

Infinite-dimensional polyhedrality

Vladimir P. Fonf
, Libor Veselý

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

28 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 language	English
Pages (from-to)	472-494
Number of pages	23
Journal	Canadian Journal of Mathematics
Volume	56
Issue number	3
DOIs	https://doi.org/10.4153/CJM-2004-022-7
State	Published - 1 Jan 2004

ASJC Scopus subject areas

General Mathematics

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AB - 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).

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Infinite-dimensional polyhedrality

Abstract

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