Contra-continuous functions and strongly-closed spaces
Open Access
- 1 January 1996
- journal article
- research article
- Published by Hindawi Limited in International Journal of Mathematics and Mathematical Sciences
- Vol. 19 (2), 303-310
- https://doi.org/10.1155/s0161171296000427
Abstract
In 1989 Ganster and Reilly [6] 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 functioncontra-continuous if the preimage of every open set is closed. A spaceis called strongly-closed if it has a finite dense subset or equivalently if every cover ofby 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.