2 results
Normality Versus Paracompactness in Locally Compact Spaces
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 74-96
- Print publication:
- 01 February 2018
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- Article
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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 ${{\omega }_{1}}$.
On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 3 / 01 September 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 579-584
- Print publication:
- 01 September 2014
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We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space that does not include a perfect pre-image of
${{\text{ }\!\!\omega\!\!\text{ }}_{1}}$ is hereditarily paracompact.
