International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 483-490
doi:10.1155/S0161171287000565

Weakly α-continuous functions

Abstract

In this paper, we introduce the notion of weakly α-continuous functions in topological spaces. Weak α-continuity and subweak continuity due to Rose [1] are independent of each other and are implied by weak continuity due to Levine [2]. It is shown that weakly α-continuous surjections preserve connected spaces and that weakly α-continuous functions into regular spaces are continuous. Corollary 1 of [3] and Corollary 2 of [4] are improved as follows: If f1:X→Y is a semi continuous function into a Hausdorff space Y, f2:X→Y is either weakly α-continuous or subweakly continuous, and f1=f2 on a dense subset of X, then f1=f2 on X.