Applications of Nano Penta (N_P) Separation axioms using N_P_ open sets

Abstract

The main goal of this paper is to use the concept _ open sets to present new classes of separation axioms in _topological spaces. Those new classes are _spaces, =0,1,2. We have studied some basic properties of these spaces. We also discussed the relationship between _spaces and Nano separation axioms spaces), =0,1,2. Furthermore the paper deals with the relationship between the separation axioms throughout kernel set associated with the closed set which used to prove some theorems related to it. The hereditary and topological properties were also discussed.