On Kasaj-b-open Sets and Kasaj-regular-open Sets in Kasaj Topological Spaces

Abstract

Recently, We defined Kasaj-topological space and weak open sets namely Kasaj-pre-open sets, Kasaj-semi-open sets, Kasaj-alpha-open sets, Kasaj-beta-open sets in Kasaj topological spaces and analyzed their basic properties. Also we defined new types of continuous functions namely Kasaj-continuous function, Kasaj-pre-continuous function, Kasaj-semi-continuous function, Kasaj-alpha-continuous function and Kasaj-beta-continuous function in Kasaj topological spaces. The purpose of this paper is to define new classes of sets called Kasaj-b-open(KS-b-open) sets, Kasaj-regular-open(KS-regular-open) sets and a new types of continuous functions namely Kasaj-b-continuous function in Kasaj topological spaces. We shall investigate their basic properties and also analyze relation among Kasaj-open sets, Kasaj-pre-open sets, Kasaj-semi-open sets, Kasaj-alpha-open sets, Kasaj-beta- open sets, Kasaj-b-open sets and Kasaj-regular-open sets.