A new approach to nearly paracompact spaces

Abstract

The pre-open sets are a generalization of open sets of topological spaces. In this paper, we introduce and study a notion of po-paracompact spaces via pre-open sets on topological spaces. We see that po-paracompact spaces are equivalent to nearly paracompact spaces. However, we find new characterizations to nearly paracompact spaces when we study it in the sense of poparacompact spaces. We see that a topological space is nearly paracompact if and only if each regularly open cover of the topological space has a locally finite pre-open refinement. We also show that four statements involving pre-open sets on an almost regular topological space are equivalent. A result on a subspace of a topological space is also obtained in term of pre-open sets.