A Proof of a Convex-Valued Selection Theorem with the Codomain of a Frechet Space
Commun. Korean Math. Soc. 2001 Vol. 16, No. 2, 277-285
Myung-Hyun Cho, Jun-Hui Kim Wonkwang University, Ehime University
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 Fr\'echet space. We also develop the properties of upper semi-continuous singlevalued mappings to those of upper semi-continuous multivalued mappings. These properties will be applied in our further considerations of selection theorems.
