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Journal of Convex Analysis 10 (2003), No. 1, 255--264
Copyright Heldermann Verlag 2003

Contracting the Maximal Points of an Ordered Convex Set

G. R. Burton
Dept. of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom

The maximal points of a nonempty closed bounded convex set in a reflexive Banach space, 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.

Keywords: Order, cone, contractible convex set, flow.

MSC 2000: 52A20, 46B20, 34C99.

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