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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 2, Pages 303-310
http://dx.doi.org/10.1155/S0161171296000427

Contra-continuous functions and strongly S-closed spaces

J. Dontchev

Department of Mathematics, University of Helsinki, Helsinki 10 00014, Finland

Received 27 June 1994

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In 1989 Ganster and Reilly [6] introduced and studied the notion of LC-continuous functions via the concept of locally closed sets. In this paper we consider a stronger form of LC-continuity called contra-continuity. We call a function f:(X,τ)→(Y,σ) contra-continuous if the preimage of every open set is closed. A space (X,τ) is called strongly S-closed if it has a finite dense subset or equivalently if every cover of (X,τ) by closed sets has a finite subcover. We prove that contra-continuous images of strongly S-closed spaces are compact as well as that contra-continuous, β-continuous images of S-closed spaces are also compact. We show that every strongly S-closed space satisfies FCC and hence is nearly compact.