# On (omega)-(beta) Continuous Functions

## Keywords:

Open set, Open functions## Abstract

A subset $A$ of a topological space $X$ is said to be $\omega \beta-$openÂ if for every $x \in A$ there exists a $\beta-$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 $\omega \beta-$continuous functions by using the notion of $\omega \beta-$open sets. In particular we say a function $f:X \to Y$Â is $\omega \beta-$continuousÂ if and only if for each $x \in X$ and each open set $V$ in $Y$ containing $f(x)$ there exists an $\omega \beta-$open set $U$ containing $x$ such that $f(U) \subseteq V$. We give some characterizations of $\omega \beta-$continuous functions, introduce and study $\omega \beta-$irresolute and $\omega \beta-$open functions. Finally, we investigate the relationship between these type of functions.

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*European Journal of Pure and Applied Mathematics*,

*5*(2), 129–140. Retrieved from https://www.ejpam.com/index.php/ejpam/article/view/1245

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