The Arkhangel'skiĭ–Tall problem under Martin’s Axiom
Fundamenta Mathematicae, Tome 149 (1996) no. 3, pp. 275-285
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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.
@article{10_4064_fm_149_3_275_285,
author = {Gary Gruenhage and Piotr Koszmider},
title = {The {Arkhangel'ski\u{i}{\textendash}Tall} problem under {Martin{\textquoteright}s} {Axiom}},
journal = {Fundamenta Mathematicae},
pages = {275--285},
publisher = {mathdoc},
volume = {149},
number = {3},
year = {1996},
doi = {10.4064/fm-149-3-275-285},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-149-3-275-285/}
}
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Gary Gruenhage; Piotr Koszmider. The Arkhangel'skiĭ–Tall problem under Martin’s Axiom. Fundamenta Mathematicae, Tome 149 (1996) no. 3, pp. 275-285. doi: 10.4064/fm-149-3-275-285
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