A Collectionwise Hausdorff, Non-Normal Moore Space

Abstract

A topological space X is said to be collectionwise Hausdorff if every discrete collection of points of X can be simultaneously separated by a collection of pairwise disjoint open sets. The question of whether there exists a collectionwise Hausdorff, non-normal Moore space was first asked by R. L. Moore. In 1964, J. M. Worrell announced that such a space did indeed exist (see [7]), but his proof has never appeared in print.