$\mu$-Paracompactness via Hereditary Classes

Abstract

The notion of paracompactness in generalized topology is introduced and studied in [5]. In this paper, we introduce and investigate the notion of $\mu$-paracompact spaces with respect to a hereditary class $\mathcal{H}$, which is a generalization of the notion of $\mu$-paracompact spaces. We study characterizations, subsets, and subspaces of $\mu\mathcal{H}$-paracompact spaces. Also, we investigate the invariants of $\mu\mathcal{H}$-paracompact spaces by functions.