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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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