The Arkhangel'skiĭ–Tall problem under Martin’s Axiom

Volume 149 / 1996

Gary Gruenhage, Piotr Koszmider 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.

Authors

  • Gary Gruenhage
  • Piotr Koszmider

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