Normality versus paracompactness in locally compact spaces

Alan Dow, Franklin D. Tall

Published 2016-07-15Version 1

This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on \omega_1, as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of \omega_1.