Zuoming Yu (2012)
Open Mathematics
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We prove that every Tychonoff strongly monotonically monolithic star countable space is Lindelöf, which solves a question posed by O.T. Alas et al. We also use this result to generalize a metrization theorem for strongly monotonically monolithic spaces. At the end of this paper, we study the extent of star countable spaces with k-in-countable bases, k ∈ ℤ.
Maddalena Bonanzinga, Filippo Cammaroto, Bruno Pansera (2011)
Open Mathematics
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The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and...
McCoy, R.A. (1980)
International Journal of Mathematics and Mathematical Sciences
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Yan-Kui Song (2013)
Open Mathematics
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We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed...
Takashi Kimura, Chieko Komoda (2008)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we give a characterization of a separable metrizable space having a metrizable S-weakly infinite-dimensional compactification in terms of a special metric. Moreover, we give two characterizations of a separable metrizable space having a metrizable countable-dimensional compactification.
Lubomyr Zdomsky (2005)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal is a lower bound of the additivity number of the -ideal generated by Menger subspaces of the Baire space, and under every subset of the real line with the property is Hurewicz, and thus it is consistent with ZFC that the property is preserved by unions of less than subsets of the real line.
Ofelia Alas, Lucia Junqueira, Jan Mill, Vladimir Tkachuk, Richard Wilson (2011)
Open Mathematics
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For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace...