### 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 language | English |
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Pages (from-to) | 255-264 |

Number of pages | 10 |

Journal | Journal of Convex Analysis |

Volume | 10 |

Issue number | 1 |

Publication status | Published - 2003 |

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## Cite this

Burton, G. R. (2003). Contracting the maximal points of an ordered convex set.

*Journal of Convex Analysis*,*10*(1), 255-264.