International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 483-490
doi:10.1155/S0161171287000565
Weakly α-continuous functions
Department of Mathematics, Yatsushiro College of Technology, Yatsushiro 866, Kumamoto, Japan
Received 28 May 1986; Revised 3 March 1987
Copyright © 1987 Takashi Noiri. 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
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.