On a Dense Gd-diagonal
A. V. Arhangel'skii, Ljubiša Kočinac (1990)
Publications de l'Institut Mathématique
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Displaying similar documents to “On Topological Spaces With Dense Completely Metrizable Subspaces”
On a Dense Gd-diagonal
On dense subspaces satisfying stronger separation axioms
Ofelia Teresa Alas, Mihail G. Tkachenko, Vladimir Vladimirovich Tkachuk, Richard Gordon Wilson, Ivan V. Yashchenko (2001)
Czechoslovak Mathematical Journal
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We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace....
On a theorem of W.W. Comfort and K.A. Ross
Aleksander V. Arhangel'skii (1999)
Commentationes Mathematicae Universitatis Carolinae
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A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is -embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group and prove that every -dense subspace of a topological group...
Tightness and resolvability
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.
A generalization of Čech-complete spaces and Lindelöf -spaces
Aleksander V. Arhangel'skii (2013)
Commentationes Mathematicae Universitatis Carolinae
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The class of -spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf -spaces, metrizable spaces with the weight , but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that -spaces are in a duality with Lindelöf -spaces: is an -space if and only if some (every) remainder of in a compactification is a Lindelöf -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math....