A generalization of paracompactness in terms of grills

Abstract

In this paper we initiate a generalized form of paracompactness via grills. We shall also define a grill-dependent regularity axiom on a topological space. From our results in such a generalized perspective, E. Michael\u27s famous theorem on regular paracompactness and certain other results like ``a $T_2$ paracompact space is regular" will follow as special cases