International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 67-73
doi:10.1155/S0161171296000117
On locally s-closed spaces
Department of Pure Mathematics, University of Calcutta 35, Bailygunge Circular Road, Calcutta 700 019, India
Received 12 October 1992; Revised 23 July 1993
Copyright © 1996 C. K. Basu. 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 the present paper, the concepts of s-closed sub-spaces, locally s-closed spaces have been introduced and characterized. We have seen that local s-closedness is a semi-regular property; the concept of s-θ-closed mapping has been introduced here and the following important properties are established:-
Let f:X→Y be an s-θ-closed surjection with s-set (Maio and Noiri [8]) point inverses. Then:
(a) If f is completely continuous (Arya and Gupta [1]) and Y is locally compact T2-space, then, X is locally s-closed.
(b) If f is ν-continuous (Ganguly and Basu [5]) and X is a locally compact T2-space, then, Y is locally s-closed.