Contracting the maximal points of an ordered convex set

Reference:

Burton, G. R., 2003. Contracting the maximal points of an ordered convex set. Journal of Convex Analysis, 10 (1), pp. 255-264.

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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.

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