Abstract

The family of regular closed subsets of a topological space is used to introduce two concepts concerning a function f from a space X to a space Y. The first of them is the notion of f being rc-continuous. One of the established results states that a space Y is extremally disconnected if and only if each continuous function from a space X to Y is rc-continuous. The second concept studied is the notion of a function f having an rc-strongly closed graph. Also one of the established results characterizes rc-compact spaces (≡S-closed spaces) in terms of functions that possess rc-strongly closed graph.