
Contracontinuous functions and strongly Sclosed spacesDOI: 10.1155/s0161171296000427 Keywords: strongly Sclosed , closed cover , contracontinuous , LCcontinuous , perfectly continuous , strongly continuous , FCC. Abstract: In 1989 Ganster and Reilly [6] introduced and studied the notion of LCcontinuous functions via the concept of locally closed sets. In this paper we consider a stronger form of LCcontinuity called contracontinuity. We call a function f:(X, ) ￠ ’(Y, ) contracontinuous if the preimage of every open set is closed. A space (X, ) is called strongly Sclosed if it has a finite dense subset or equivalently if every cover of (X, ) by closed sets has a finite subcover. We prove that contracontinuous images of strongly Sclosed spaces are compact as well as that contracontinuous, 2continuous images of Sclosed spaces are also compact. We show that every strongly Sclosed space satisfies FCC and hence is nearly compact.
