On some fan-tightness type properties

J. Valuyeva

Displaying similar documents to “On some fan-tightness type properties”

Spaces of continuous characteristic functions

Raushan Z. Buzyakova (2006)

Commentationes Mathematicae Universitatis Carolinae

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We show that if $X$ is first-countable, of countable extent, and a subspace of some ordinal, then $C_{p} (X, 2)$ is Lindelöf.

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...

Countable fan-tightness versus countable tightness

Aleksander V. Arhangel&#039;skii, Angelo Bella (1996)

Commentationes Mathematicae Universitatis Carolinae

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Countable tightness is compared to the stronger notion of countable fan-tightness. In particular, we prove that countable tightness is equivalent to countable fan-tightness in countably compact regular spaces, and that countable fan-tightness is preserved by pseudo-open compact mappings. We also discuss the behaviour of countable tightness and of countable fan-tightness under the product operation.