International Journal of Mathematics and Mathematical Sciences 
Volume 28 (2001), Issue 8, Pages 469-478
doi:10.1155/S0161171201006640

Slightly β-continuous functions

Takashi Noiri

 Department of Mathematics, Yatsushiro College of Technology, Kumamoto, Yatsushiro 866-8501, Japan
Received 1 September 2000; Revised 30 January 2001

Abstract

We define a function f:X→Y to be slightly β-continuous if for every clopen set V of Y, f−1(V)⊂Cl(Int(Cl(f−1(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.