Displaying similar documents to “Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces”

Locally compact perfectly normal spaces may all be paracompact

Paul B. Larson, Franklin D. Tall (2010)

Fundamenta Mathematicae

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We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact...

Covering the real line with translates of a zero-dimensional compact set

András Máthé (2011)

Fundamenta Mathematicae

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We construct a compact set C of Hausdorff dimension zero such that cof(𝒩) many translates of C cover the real line. Hence it is consistent with ZFC that less than continuum many translates of a zero-dimensional compact set can cover the real line. This answers a question of Dan Mauldin.

The union of two D-spaces need not be D

Dániel T. Soukup, Paul J. Szeptycki (2013)

Fundamenta Mathematicae

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We construct from ⋄ a T₂ example of a hereditarily Lindelöf space X that is not a D-space but is the union of two subspaces both of which are D-spaces. This answers a question of Arhangel'skii.