On $omegabeta$−continuous functions

Abstract

A subset A of topological space (X,) is said to be $omega beta$ −open [3] if for every x ∈ A there exists an $beta$ −open set U containing x such that U − A is a countable. In this paper, we introduce and study new class of function which is $omega beta$ −continuous functions by using the notion of $omega beta$ −open sets. This new class of function defines as a function f : (X,)→(Y,$sigma$) from a topological space (X,) into a topological space (Y,$sigma$) is $omega beta$ −Continuous function if and only if for each x ∈ X and each open set V in (Y,$sigma$) containing f (x) there exists an $beta$ −open set U containing x such that f (U) ⊆ V. We give some characterizations of $omega beta$ −Continuous functions, define $omega beta$ −irresolute and $omega beta$ −open function. Finally, we find relationship between these type of function.