Pmea and First Countable, Countably Paracompact Spaces

Abstract

The Product Measure Extension Axiom is used to prove a "$\theta$-expandable" type property for first countable, countably paracompact (countably metacompact) spaces. Among other results, it follows (under PMEA) that countably paracompact Moore spaces are metrizable, and first countable, countably paracompact Hausdorff spaces are strongly collectionwise normal with respect to compact sets.