On gso-Closed Sets in Topological Spaces

Abstract

In this paper, a new kind of closed sets called generalized semi open-closed sets (briefly gso-closed sets) are introduced in topological spaces. A subset A of a topological space X is called a gsoclosed set if A is both a g-closed set and a semi-open set in X. The properties of the gso-closed sets are investigated and they are compared with the existing relevant generalized closed sets. The generalized semi-open continuous function between topological spaces are also defined and their properties are investigated.

gr-connectedness in Topological Spaces

“…Data structure is important in the applications on the computer which relates real topological situation. Connectedness and compactness were studied by Whyburn G. T [2], considering the assumption of Hausdorff.The basic properties of connectedness had been discussed through many researchers [3][4][5][6][7][8][9][10][11][12]. Mathematicians are motivated through the notions of connectedness to extend the existing concepts.…”

Study of α*-Homeomorphisms by α*-closed Sets

“…With the introduction of this generalized closed sets, many authors introduced different type of generalized closed sets and studied their properties. The ωclosed set [2], semi-generalized closed (briefly sg-closed) set [3], generalized α-closed (briefly gα-closed) set [4], regular generalized closed (briefly rg-closed) set [5], beta weakly generalzed closed (briefly βwg-closed) set [6], generalized semi open-closed (briefly gso-closed) set [7] are *Corresponding author: E-mail: kvithy83@gmail.com some of the generalized closed sets in the literature.…”