Quasicontinuous selections of upper continuous set-valued mappings. (English) Zbl 1097.54023

Cao, Jiling; Moors, Warren B.

Real Anal. Exch. 31(2005-2006), No. 1, 63-71 (2006).

In this paper a Matejdes theorem on quasicontinuous selection is extended to the case of upper Baire continuous set valued mappings with nonempty compact values \(T:X\rightarrow 2^{Y}\), where \(X\) is an arbitrary topological space and \(Y\) a regular \(T_{1}\) space. Moreover, the authors prove a quasicontinuous selection theorem for strongly injective upper semicontinuous set-valued mappings with nonempty closed values.

Reviewer: Ryszard Pawlak (Łódź)

MSC:

54C65	Selections in general topology
54C60	Set-valued maps in general topology
26E25	Set-valued functions

Keywords:

set valued mapping; quasicontinuity, selection; upper Baire continuity