International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 303-310
Contra-continuous functions and strongly -closed spaces
Department of Mathematics, University of Helsinki, Helsinki 10 00014, Finland
Received 27 June 1994
Copyright © 1996 J. Dontchev. 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.
In 1989 Ganster and Reilly  introduced and studied the notion of -continuous
functions via the concept of locally closed sets. In this paper we consider a stronger form of
-continuity called contra-continuity. We call a function contra-continuous if the
preimage of every open set is closed. A space is called strongly -closed if it has a finite dense
subset or equivalently if every cover of by closed sets has a finite subcover. We prove that contra-continuous
images of strongly -closed spaces are compact as well as that contra-continuous, -continuous images of -closed spaces are also compact. We show that every strongly -closed space
satisfies FCC and hence is nearly compact.