Υ_G-Operator in grill N-topology

Abstract

In 2017, Lellis Thivagar et al. introduced a closure operator $N\tau_G$-$cl$  by using the local function $\Phi_G$ in grill $N$-topology. In this article, we introduce a new operator $\Upsilon_G$ in the same topological space. We study the properties of this new operator which helps us to derive a few equivalent expressions and a characterizing condition, in terms of $\Upsilon_G$. Then a  suitability condition for a grill in $N$-topological space $X$ is formulated. Also, we discuss the characterizing condition for the discussed suitability condition. In addition, we introduce and study $\widehat{\Upsilon}_{G}–$sets and utilize the $\Upsilon_G$-operator to define a generalized open set and their properties.