Monotone normality

Abstract

Two theorems are given analyzing the possible refinements of open covers of a monotonically normal space X. The first shows that X is paracompact if and only if X has no closed subset homeomorphic to a stationary subset of a regular uncountable cardinal. The second shows that if U is an open cover of X, then U has a σ-disjoint open, partial refinement V such that X- U V is the union of a discrete family of stationary subsets of regular uncountable cardinals.