English

Normality versus paracompactness in locally compact spaces

General Topology 2019-08-15 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1607.04364,
  title  = {Normality versus paracompactness in locally compact spaces},
  author = {Alan Dow and Franklin D. Tall},
  journal= {arXiv preprint arXiv:1607.04364},
  year   = {2019}
}
R2 v1 2026-06-22T14:55:25.098Z