SαRPS-SEPARATION AXIOMS IN TOPOLOGICAL SPACES

Abstract

The investigation of generalized closed sets has led to several new interesting concepts. There is a vast progress occurred in the field of generalized open sets (compliment of generalized closed sets) which became the base for separation axioms in the respective context. In recent years there have been a considerable number of papers considering separation properties, essentially defined by replacing open sets by generalized open sets. We introduced semi -regular pre-semi- closed sets in topological spaces and semi -regular pre-semi open sets in topological spaces and we have studied the basic properties. Also we have given the relationship between these sets with some other existing generalized sets in topological spaces. Then we introduced semi -regular pre-semi continuous and semi -regular pre-semi irresolute functions in topological spaces and characterize the basic properties. Also we have given the relationship between these continuous functions with some other existing continuous functions. After that, we introduced contra -continuous functions in topological spaces. In this paper, we introduce some new type of separation axioms and study some of their basic properties using -open set. First we introduce -T₀, - T₁ and - T₂ spaces and characterize their properties with -continuous, -irresolute and -open functions, -closure and                      -neighbourhoods. Next we introduce -Tb, -Tâ…“, -T½ and -T¾ spaces and the connections between these separation axioms are also investigated. Also we give a diagram which represents the relationships between -Tb, -T½, -Tâ…“, Tb, T, T and Tb spaces. Next we introduce -R₀ and -R₁ spaces and characterize the properties of these spaces with -T₀, - T₁ and - T₂ spaces ,-kernal and -closure.

Keywords:

-T₀, - T₁, - T₂, -Tb, -Tâ…“, -T½, -T¾, -R₀, -R₁.