On locally s-closed spaces

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.