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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 72, Pages 4547-4555
http://dx.doi.org/10.1155/S0161171203203410

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

Department of Mathematics, Faculty of Science, Yarmouk University, Irbid, Jordan

Received 20 March 2002

Copyright © 2003 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

The family of regular closed subsets of a topological space is used to introduce two concepts concerning a function f from a space X to a space Y. The first of them is the notion of f being rc-continuous. One of the established results states that a space Y is extremally disconnected if and only if each continuous function from a space X to Y is rc-continuous. The second concept studied is the notion of a function f having an rc-strongly closed graph. Also one of the established results characterizes rc-compact spaces (S-closed spaces) in terms of functions that possess rc-strongly closed graph.