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Local cardinal functions of H-closed spaces

Angelo Bella, Jack R. Porter (1996)

Commentationes Mathematicae Universitatis Carolinae

The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between H-closed and minimal Hausdorff spaces. An H-closed space X is produced with the properties that | X | > 2 2 ψ ( X ) and ψ ¯ ( X ) > 2 ψ ( X ) .

Locally compact perfectly normal spaces may all be paracompact

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

Fundamenta Mathematicae

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 At a crucial step we use some still unpublished results announced by Todorcevic.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 Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...

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