Countable And Uncountable Covers
H. P. Tan (1973)
Publications de l'Institut Mathématique
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H. P. Tan (1973)
Publications de l'Institut Mathématique
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István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2007)
Fundamenta Mathematicae
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We answer several questions of V. Tkachuk [Fund. Math. 186 (2005)] by showing that ∙ there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the minimum order of a π-base of the space can be made arbitrarily large); ∙ if there is a κ-Suslin line then there is a first countable GO-space of cardinality κ⁺ in which the order of any π-base is at least κ; ∙ it is consistent to have a...
Vladimir Vladimirovich Tkachuk (1988)
Commentationes Mathematicae Universitatis Carolinae
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Aleksander V. Arhangel'skii, Angelo Bella (1996)
Commentationes Mathematicae Universitatis Carolinae
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Countable tightness is compared to the stronger notion of countable fan-tightness. In particular, we prove that countable tightness is equivalent to countable fan-tightness in countably compact regular spaces, and that countable fan-tightness is preserved by pseudo-open compact mappings. We also discuss the behaviour of countable tightness and of countable fan-tightness under the product operation.
Eric van Douwen, Teodor Przymusiński (1979)
Fundamenta Mathematicae
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