\Gamma-P_S-functions in topological spaces

Abstract

This paper introduces some new classes of functions called γ-P Scontinuous, β-P S-open and β-P S-closed using γ-P S-open set and γ-P Sclosed set. In addition, some properties and characterizations of these functions are given. The result shows that γ-P S-continuous function and γ-continuous function are independent.

gamma-P_S-GENERALIZED CLOSED SETS AND gamma-P_S-T_1/2 SPACES

“…the τ γ -P S -interior of A is defined as the union of all γ-P S -open sets of X contained in A and it is denoted by τ γ -P S Int(A) [2].…”

“…the τ γ -P S -closure, τ γ -preclosure and τ α−γ -closure of A is defined as the intersection of all γ-P S -closed, γ-preclosed and α-γ-closed sets of X containing A and it is denoted by τ γ -P S Cl(A) [2], τ γ -pCl(A) [9] and τ α−γ -Cl(A) [7], respectively.…”

“…Definition 2.12. [3] Let (X, τ ) and (Y, σ) be two topological spaces and γ be an operation on τ . A function f : (X, τ ) → (Y, σ) is called γ-P S -closed if the image of every closed set in Y is γ-P S -closed set in X.…”

“…[2] Let (X, τ ) be a topological space and γ be an operation on τ . If X is γ-semi-T 1 , then the notion of γ-P S -open set and γ-preopen set coincide, or this means that the notion of γ-P S -closed set and γ-preclosed set coincide.…”

“…Recently, Asaad, Ahmad and Omar [1] defined the notion of γ-regular-open sets which lies strictly between the classes of γ-open set and γ-clopen set. They also introduced a new class of sets called γ-P S -open sets, and they also defined γ-P S -operations and their properties [2].…”