A new way to find compact zero-dimensional first countable preimages of first countable compact spaces
Vladimir Vladimirovich Tkachuk (1988)
Commentationes Mathematicae Universitatis Carolinae
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Vladimir Vladimirovich Tkachuk (1988)
Commentationes Mathematicae Universitatis Carolinae
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H. P. Tan (1973)
Publications de l'Institut Mathématique
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Eric van Douwen, Teodor Przymusiński (1979)
Fundamenta Mathematicae
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Angelo Bella, Viacheslav I. Malykhin (1998)
Commentationes Mathematicae Universitatis Carolinae
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We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.
Victor Harnik, Mark Nadel, Jonathan Stavi (1986)
Fundamenta Mathematicae
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Kyriakos Keremedis, Evangelos Felouzis, Eleftherios Tachtsis (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that: (1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T₂ topological space is zero-dimensional. (2) If every countable union of countable sets of reals is countable, then a countable compact T₂ space is scattered iff it is metrizable. (3) If the real line ℝ can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional...
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...
F. Harary, A.J. Schwenk, R.L. Scott (1972)
Publications de l'Institut Mathématique [Elektronische Ressource]
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