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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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.
Aleksander V. Arhangel'skii (2010)
Commentationes Mathematicae Universitatis Carolinae
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Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen...
P. Moody, G. Reed, A. Roscoe, P. Collins (1991)
Fundamenta Mathematicae
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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...
Baboolal, D., Backhouse, J., Ori, R.G. (1990)
International Journal of Mathematics and Mathematical Sciences
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