Geodesic
Infinite-Dimensional Polyhedrality
Canadian journal of mathematics, Tome 56 (2004) no. 3, pp. 472-494

Voir la notice de l'article provenant de la source Cambridge University Press

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).
DOI : 10.4153/CJM-2004-022-7
Mots-clés : 46B20, 46B03, 46B04, 52B99 
Fonf, Vladimir P.; Veselý, Libor. Infinite-Dimensional Polyhedrality. Canadian journal of mathematics, Tome 56 (2004) no. 3, pp. 472-494. doi: 10.4153/CJM-2004-022-7
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