- MICHAEL'S SELECTION THEORIES AND THEIR APPLICATIONS
- CHO, MYUNG HYUN ;
- Honam Mathematical Journal, volume 20, issue 1, 1998, Pages 135~145
Abstract
In this paper, we focus on the convex-valued selection theorem out of four main selection theorems; zero-dimensional, convex-valued, compact-valued, finite-dimensional theorems based on Michael's papers. We prove some theorems about lower semi-continuous set-valued mappings, and derive some applications to closed continuous set-valued mappings and to functional analysis. We also give a partial solution to the open problem posed by Engelking, Heath, and Michael.