In this paper, we introduce a new class of sets called ψg*-closed sets in topological spaces. A subset A of X is said to be ψg*-closed if ψCl(A) U whenever A U and U is g*-open in X. Also we study some of its basic properties and investigate the relationship with other existing closed sets in topological space. As an application, we introduce four new spaces namely Tψg*-space and gTψg*-space

In this paper, we introduce the notion of Pythagorean Anti fuzzy graph. We then define the Cartesian product and Lexicographic product on Pythagorean Anti fuzzy graph. It is proved that Cartesian product of two Pythagorean Anti fuzzy graphs is Pythagorean Anti fuzzy graph and Lexicographic product of two Pythagorean Anti fuzzy graphs is Pythagorean Anti fuzzy graph. In general, Cartesian product and lexicographic product of two regular Pythagorean Anti fuzzy graphs need not be Pythagorean Anti fuzzy graph. Necessary and sufficient conditions for Cartesian and lexicographic product of two Pythagorean Anti fuzzy graphs to be regular are determined. Further, we define the concept of isomorphism on Pythagorean Anti fuzzy graph with suitable example.

In this paper, we introduce a new function called tri-ĝ continuous in tri-topological spaces. A map f : X → Y is called tri-ĝ continuous if f-1(V) is tri-ĝ closed in X for each tri-closed set V in Y. Also we define, quasi tri-ĝ. perfectly tri-ĝ, contra tri-ĝ, totally tri-ĝ and strongly tri-ĝ continuous maps are introduced and some of their properties are studied.

In this present paper, we introduce and study some soft topological properties of soft ℳ-border, soft ℳ-exterior and soft ℳ-boundary of a soft set using the concept of soft ℳ-open sets and soft ℳ-closed sets and also studied the other property of the well known notion of soft ℳ-interior, ℳ-closure.