rc-continuous functions and functions with rc-strongly closed graph

摘要

The family of regular closed subsets of a topological space isused to introduce two concepts concerning a functionffrom aspaceXto a spaceY. The first of them is the notion offbeing rc-continuous. One of the established results states that aspaceYis extremally disconnected if and only if eachcontinuous function from a spaceXtoYis rc-continuous. Thesecond concept studied is the notion of a functionfhaving anrc-strongly closed graph. Also one of the established resultscharacterizes rc-compact spaces (≡S-closed spaces) interms of functions that possess rc-strongly closed graph.