A PROOF OF A CONVEX-VALUED SELECTION THEOREM WITH THE CODOMAIN OF A FRECHET SPACE

  • Cho, Myung-Hyun (Department of Mathematics, Wonkwang University) ;
  • Kim, Jun-Hui (Department of Mathematics Sciences, Faculty of Science, Ehime University)
  • Published : 2001.04.01

Abstract

The purpose of this paper is to give a proof of a generalized convex-valued selection theorem which is given by weakening a Banach space to a completely metrizable locally convex topological vector space, i.e., a Frechet space. We also develop the properties of upper semi-continuous singlevalued mapping to those of upper semi-continuous multivalued mappings. These properties wil be applied in our further consideraations of selection theorems.

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