The Arkhangel’skiĭ–Tall problem: a consistent counterexample

Volume 149 / 1996

Gary Gruenhage, Piotr Koszmider Fundamenta Mathematicae 149 (1996), 143-166 DOI: 10.4064/fm-149-2-143-166


We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel'skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in $[ω]^ω$, and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.


  • Gary Gruenhage
  • Piotr Koszmider

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