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Normality Versus Paracompactness inLocally Compact Spaces

Published online by Cambridge University Press:  20 November 2018

Alan Dow  and
Franklin D. Tall
Alan Dow
Affiliation:
Department of Mathematics and Statistics, University of North Carolina, Charlotte, North Carolina 28223, USA e-mail: adow@uncc.edu
Franklin D. Tall
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON MSS 2E4 e-mail: f.tall@math.utoronto.ca
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Abstract

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This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on ${{\omega }_{1}}$ , as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the consistent characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of ${{\omega }_{1}}$ .

Keywords

54A3554D2054D4503E3503E5003E5503E57normalparacompactlocally compactcountably tightcollectionwise Hausdorffforcing with a coherent Souslin treeMartin's MaximumPFA(S)[S]Axiom Rmoving off property

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 1 , 01 February 2018 , pp. 74 - 96
Copyright
Copyright © Canadian Mathematical Society 2018

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