Limit Points and Separation Axioms with Respect to Supra Semi-open Sets

Abstract

Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems, or constructing some counterexamples whom show the interrelations between certain topological concepts, or preserving some properties under fewer conditions of those on topology. To contribute this research area, in this paper, we establish some new concepts on supra topological spaces using supra semi-open sets and give some characterizations of them. First, we introduce a concept of supra semi limit points of a set and study main properties, in particular, on the spaces that possess the difference property. Second, we define and investigate new separation axioms, namely supra semi Ti-spaces (i = 0, 1, 2, 3, 4) and give complete descriptions for each one of them. We provide some examples to show the relationships between them as well as with STi-space.

β*-Regular supra topological spaces

“…M. Al-shami etal . [5] evolved the last concept and presented the notations of supra semi. neighborhood and supra semi T1-space.…”

“…supra semi * . closed [5] ,supra semi * .open [5]) if the image of a supra closed is supra closed (resp. the image of a supra semi-closed is supra semi-closed , the image of a supra semi-open is supra semi-open ) .…”

Note on (i, j) − mX − β−Exterior Sets in Biminimal 3 Structure Spaces

“…al. [1] focused their attention on topology space. The concept of supra semi limit points of a set and new types of separation axioms using supra semi-open sets were introduced to minimize the conditions of topology for other reasons.…”

Applications of some operators on supra topological spaces

“…Al-shami [23] introduced the concept of paracompactness on STSs and explored main properties. Recently, the authors of [24][25][26][27] have employed some generalizations of supra open sets given in [28][29][30][31] to study limit points and separation axioms on STSs. They have provided various interesting examples to explain the given relationships and results.…”