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International Journal of Mathematics and Mathematical Sciences
Volume 28, Issue 8, Pages 469-478
http://dx.doi.org/10.1155/S0161171201006640

Slightly β-continuous functions

Department of Mathematics, Yatsushiro College of Technology, Kumamoto, Yatsushiro 866-8501, Japan

Received 1 September 2000; Revised 30 January 2001

Copyright © 2001 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

We define a function f:XY to be slightly β-continuous if for every clopen set V of Y, f1(V)Cl(Int(Cl(f1(V)))). We obtain several properties of such a function. Especially, we define the notion of ultra-regularizations of a topology and obtain interesting characterizations of slightly β-continuous functions by using it.