Quasicontinuous selections of upper continuous set-valued mappings.

Abstract

In this paper, we extend a theorem of Matejdes on quasicontinuous selections of upper Baire continuous set-valued mappings from compact (or separable) metric range spaces to regular $T_1$ range spaces. In addition, we also prove a quasicontinuous selection theorem for a special class of upper semicontinuous set-valued mappings.