Displaying similar documents to “AB-compacta”

AB-compacta.

Gorelic, Isaac, Juhász, István (2008)

Commentationes Mathematicae Universitatis Carolinae

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AB-compacta

Isaac Gorelic, István Juhász (2008)

Commentationes Mathematicae Universitatis Carolinae

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We define a compactum X to be AB-compact if the cofinality of the character χ ( x , Y ) is countable whenever x ∈ Y and Y ⊂ X . It is a natural open question if every AB-compactum is necessarily first countable. We strengthen several results from [Arhangel’skii and Buzyakova, Convergence in compacta and linear Lindelöfness, Comment. Math. Univ. Carolin. 39 (1998), no. 1, 159–166] by proving the following results. • Every AB-compactum is countably tight. • If 𝔭 = 𝔠 then every AB-compactum is Frèchet-Urysohn....

On absolutely submetrizable spaces

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. ...

Closed embeddings into complements of Σ -products

Aleksander V. Arhangel'skii, Miroslav Hušek (2008)

Commentationes Mathematicae Universitatis Carolinae

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In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a Σ -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin...