Separating sets by lower and upper semicontinuous functions with a closed graph

Abstract

In this paper we characterize the pairs (A^- ;A⁺) of disjoint subsets of perfectly normal topological space which can be separated by a lower and an upper semicontinuous function with a closed graph.

Mathematics Subject Classification (2010): 54C30, 26A15, 54C08, 54C20.

Key words: Functions with a closed graph, lower semicontiuous functions, upper semi- contiuous functions, Urysohn lemma, separating sets, extensions of functions.