Displaying similar documents to “New types of almost countable dense homogeneous space.”

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.

Note on countable unions of Corson countably compact spaces

Ondřej F. K. Kalenda (2004)

Commentationes Mathematicae Universitatis Carolinae

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We show that a compact space K has a dense set of G δ points if it can be covered by countably many Corson countably compact spaces. If these Corson countably compact spaces may be chosen to be dense in K , then K is even Corson.

About remainders in compactifications of homogeneous spaces

D. Basile, Angelo Bella (2009)

Commentationes Mathematicae Universitatis Carolinae

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We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space X , every remainder of X is either realcompact and meager or Baire. In addition we show that two other recent dichotomy theorems for remainders of topological groups due to Arhangel’skii cannot be extended to homogeneous spaces.

A construction of a Fréchet-Urysohn space, and some convergence concepts

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...