The Arkhangel'skiĭ–Tall problem under Martin’s Axiom
Volume 149 / 1996
Fundamenta Mathematicae 149 (1996), 275-285
DOI: 10.4064/fm-149-3-275-285
Abstract
We show that MA$_{σ-centered}(ω_1)$ implies that normal locally compact metacompact spaces are paracompact, and that MA($ω_1$) implies normal locally compact metalindelöf spaces are paracompact. The latter result answers a question of S. Watson. The first result implies that there is a model of set theory in which all normal locally compact metacompact spaces are paracompact, yet there is a normal locally compact metalindelöf space which is not paracompact.
