On $g \mu$-Paracompact Sets

In this work, we use the notion of the $g \mu$-paracompact space \cite{ADeb} to introduce two types of $g \mu$-paracompact sets called $\alpha$-$g \mu$-paracompact and $\beta$-$g \mu$-paracompact. We show that every $\alpha$-$g \mu$-paracompact set is $\beta$-$g \mu$-paracompact and if a generalized topological space $(S,\mu)$ is $g \mu$-paracompact, then every $\mu$-closed subset in $(S,\mu)$ is $\alpha$-$g \mu$-paracompact while every $\mu g$-closed subset in $(S, \mu)$ is $\beta$-$g \mu$-paracompact. Finally, we introduce the notion of $co$-$\alpha$-$g\mu$-paracompact set as an application of $\alpha$-$g\mu$-paracompact and study some of its features.