On closed convex sets without boundary rays and asymptotes |
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Authors: | A. Auslender and P. Coutat |
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Affiliation: | (1) U.F.R. Mathématiques & Informatique, Université de Paris I Panthéon-Sorbonne, 90 rue de Tolbiac, 75634 Paris cedex 13, France |
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Abstract: | We study in finite-dimensional spaces the class of closed convex sets without boundary rays and asymptotes, denoted by and introduced by D. Gale and V. Klee. These sets, not necessarily bounded, enjoy many properties satisfied by compacts sets. New properties of this class are given and convergence analysis of this class is investigated. We also introduce the class of closed convex proper functions which have an epigraph in and we give some properties of these functions. |
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Keywords: | 52A20 |
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