(untitled) (European Journal of Pure and Applied Mathematics, 2012)
A subset A of a topological space X is said to be ω β-openÂ if for every x A there exists a β-open set U containing x such that U-A is a countable. In this paper, we introduce and study a new class of functionsÂ called ω β-continuous functions by using the notion of ω β-open sets. In particular we say a function f:X → YÂ is ω β-continuousÂ if and only if for each x X and each open set V in Y containing f(x) there exists an ω β-open set U containing x such that f(U) V. We give some characterizations of ω β-continuous functions, introduce and study ω β-irresolute and ω β-open functions. Finally, we investigate the relationship between these type of functions.