Contracting the maximal points of an ordered convex set

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Abstract

The maximal points of a nonempty closed bounded convex set in a reflexive Banach spare, relative to an ordering defined by a locally uniformly convex cone, are studied. The set of maximal points is proved to be contractible, and sufficient conditions are found for it to be contractible by a homotopy with the semigroup property, or by the flow of an ordinary differential equation.
Original languageEnglish
Pages (from-to)255-264
Number of pages10
JournalJournal of Convex Analysis
Volume10
Issue number1
Publication statusPublished - 2003

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