Operation on Fine Topology

Abstract

This paper introduces the concept of an operation $\gamma$ on $\tau_f$. Using this operation, we define the concept of $f_\gamma$-open sets, and study some of their related notions. Also, we introduce the concept of $f_\gamma g$.closed sets and then study some of its properties. Moreover, we introduce and investigate some types of $f_\gamma$-separation axioms and $f_{\gamma\beta}$-continuous functions by utilizing the operation $\gamma$ on $\tau_f$. Finally, some basic properties of functions with $f_\beta$-closed graphs have been obtained.