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On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces

  Published:2014-04-21
 Printed: Sep 2014
  • Paul Larson,
    Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3
  • Franklin D. Tall,
    Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3
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Abstract

We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of $\omega_1$ is hereditarily paracompact.
Keywords: locally compact, hereditarily normal, paracompact, Axiom R, PFA$^{++}$ locally compact, hereditarily normal, paracompact, Axiom R, PFA$^{++}$
MSC Classifications: 54D35, 54D15, 54D20, 54D45, 03E65, 03E35 show english descriptions Extensions of spaces (compactifications, supercompactifications, completions, etc.)
Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
Noncompact covering properties (paracompact, Lindelof, etc.)
Local compactness, $\sigma$-compactness
Other hypotheses and axioms
Consistency and independence results
54D35 - Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54D20 - Noncompact covering properties (paracompact, Lindelof, etc.)
54D45 - Local compactness, $\sigma$-compactness
03E65 - Other hypotheses and axioms
03E35 - Consistency and independence results
 

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