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For $\emptyset \neq M \subseteq ω^{*}$ , we say that $X$ is quasi $M$ -compact, if for every $f : ω \to X$ there is $p \in M$ such that $\bar{f} (p) \in X$ , where $\bar{f}$ is the Stone-Čech extension of $f$ . In this context, a space $X$ is countably compact iff $X$ is quasi $ω^{*}$ -compact. If $X$ is quasi $M$ -compact and $M$ is either finite or countable discrete in $ω^{*}$ , then all powers of $X$ are countably compact. Assuming $C H$ , we give an example of a countable subset $M \subseteq ω^{*}$ and a quasi $M$ -compact space $X$ whose square is not countably compact, and show that in a model of A. Blass and S. Shelah every quasi...

Countable dense homogeneous filters and the Menger covering property

Dušan Repovš, Lyubomyr Zdomskyy, Shuguo Zhang (2014)

Fundamenta Mathematicae

We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any n ∈ ω ∪ {∞} an n-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.

Countable paracompactness of inverse limits and products

Keiô Nagami (1972)

Fundamenta Mathematicae

Countably $I$ -compact spaces.

Al-Nashef, Bassam (2001)

International Journal of Mathematics and Mathematical Sciences

Countably $S$ -closed spaces

Karin Dlaska, Nurettin Ergun, Maximilian Ganster (1994)

Mathematica Slovaca

Countably z-compact spaces

A.T. Al-Ani (2014)

Archivum Mathematicum

In this work we study countably z-compact spaces and z-Lindelof spaces. Several new properties of them are given. It is proved that every countably z-compact space is pseuodocompact (a space on which every real valued continuous function is bounded). Spaces which are countably z-compact but not countably compact are given. It is proved that a space is countably z-compact iff every countable z-closed set is compact. Characterizations of countably z-compact and z-Lindelof spaces by multifunctions...

Covering properties in countable products, II

Sachio Higuchi, Hidenori Tanaka (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If $Y$ is a perfect subparacompact space and ${X_{n} : n \in ω}$ is a countable collection of subparacompact Čech-scattered spaces, then the product $Y \times \prod_{n \in ω} X_{n}$ is subparacompact and (2) If ${X_{n} : n \in ω}$ is a countable collection of metacompact Čech-scattered spaces, then the product $\prod_{n \in ω} X_{n}$ is metacompact.

We study the class of descriptive compact spaces, the Banach spaces generated by descriptive compact subsets and their relation to renorming problems.

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Displaying 101 – 120 of 477

Concerning product of paracompact spaces

Concerning two covering properties

Condiciones suficientes para la paracompacidad-c. Aplicación a un teorema de metrización.

Continuous extensions: answer to a question of Hanner

Contra-continuous functions and strongly $S$ -closed spaces.

Countable And Uncountable Covers

Countable and Uncountable covers.

Countable compactness and $p$ -limits

Countable dense homogeneous filters and the Menger covering property

Countable paracompactness of inverse limits and products

Countably $I$ -compact spaces.

Countably $S$ -closed spaces

Countably z-compact spaces

Covering properties in countable products, II

C-scattered and paracompact spaces

Dedekind-Endlichkeit und Wohlordenbarkeit.

Descriptive compact spaces and renorming

Dimensions and partitions of unity

Dyadic mappings and dyadic superparacompact topological groups.

Each concrete category has a representation by $T_{2}$ paracompact topological spaces

Currently displaying 101 – 120 of 477