Analysis of Some Generalized Closed Sets Using n star Closure Operator

Abstract

Topology is broadly considered to be a part of Mathematics through the examination started by the incredible mathematician Henri Poincare in the nineteenth century. Topology has been created as a field of study with the rudimentary knowledge of geometry and set theory. The topological structures are appropriate for the quantitative information as well as for the subjective information. So the ideas of sets and capacities in topological spaces are exceptionally evolved and utilized in numerous pure and applied mathematics. The notion of open sets is a powerful tool for defining a topological space. In 1937, the idea of regular open sets was initiated by Stone which is a stronger form of open sets. In 1968, Velicko proposed -open sets which are stronger than open sets. In order to extend some important properties of closed sets to a larger family of sets, in 1970, Norman Levine introduced the concept of a generalised closed sets which are called as g-closed sets. In 1984,Dunham has established a generalized closure operator using Levine s generalized closed sets as Cl*. In 2016, Annalakshmi has introduced regular*-open sets using the operator Cl*. The spaces in which the concepts of g-closed and closed sets coincide are called T1/2-spaces. In the year 1975,Maheswari and Prasad introduced semi-T1-spaces.The notion of semi-T1/2-spaces was given by Bhattacharaya in 1987. In 1993, Tb, Td -spaces are introduced by Devi. Molodtsov initiated the concept of soft set theory as a completely generic mathematical tool for modeling with uncertainty problems. Soft systems provide a general framework with the involvement of parameters. In recent years the development in the field of soft set theory and its applications have been taking place in a rapid pace. Shabir and Naz introduced the notion of soft topological spaces which are defined over an initial universe with a fixed set of parameters. Kannan introduced soft g-closed sets in soft topological spaces. Intensive research on the field of soft g-closed sets was done as the th