Distinguishing Lindelöfness and inverse Lindelöfness
Viacheslav I. Malykhin (1995)
Commentationes Mathematicae Universitatis Carolinae
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On a Hausdorff inverse Lindelöf non Lindelöf topology has been constructed.
Viacheslav I. Malykhin (1995)
Commentationes Mathematicae Universitatis Carolinae
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On a Hausdorff inverse Lindelöf non Lindelöf topology has been constructed.
Raushan Z. Buzyakova (2006)
Commentationes Mathematicae Universitatis Carolinae
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We introduce a notion of absolute submetrizability (= ``every Tychonoff subtopology is submetrizable'') and investigate its behavior under basic topological operations. The main result is an example of an absolutely submetrizable space that contains an uncountable set of isolated points (hence the space is neither separable nor hereditarily Lindelöf). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums. ...
Eric van Douwen, Teodor Przymusiński (1979)
Fundamenta Mathematicae
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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...
Nina M. Roy (1989)
Publicacions Matemàtiques
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In this expository paper it is shown that Martin's Axiom and the negation of the Continuum Hypothesis imply that the product of ccc spaces is a ccc space. The Continuum Hypothesis is then used to construct the Laver-Gavin example of two ccc spaces whose product is not a ccc space.
McIntyre, David W. (2002)
International Journal of Mathematics and Mathematical Sciences
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