Infinite-Dimensional Polyhedrality
[摘要] This paper deals with generalizations of the notion of a polytope to infinitedimensions. The most general definition is the following: a bounded closedconvex subset of a Banach space is called a emph{polytope} if each of itsfinite-dimensional affine sections is a (standard) polytope.We study the relationships between eight known definitions of infinite-dimensionalpolyhedrality. We provide a complete isometric classification of them, which givessolutions to several open problems. An almost complete isomorphic classificationis given as well (only one implication remains open).
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[效力级别] [学科分类] 数学(综合)
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