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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 compactness of lexicographic products of GO-spaces

Nobuyuki Kemoto (2019)

Commentationes Mathematicae Universitatis Carolinae

We characterize the countable compactness of lexicographic products of GO-spaces. Applying this characterization about lexicographic products, we see: $\circ$ \circ ...

Countable Hausdorff spaces with countable weight

Věra Trnková (1985)

Commentationes Mathematicae Universitatis Carolinae

Countable paracompactness of inverse limits and products

Keiô Nagami (1972)

Fundamenta Mathematicae

Countable products of Čech-scattered supercomplete spaces

Aarno Hohti, Zi Qiu Yun (1999)

Czechoslovak Mathematical Journal

We prove by using well-founded trees that a countable product of supercomplete spaces, scattered with respect to Čech-complete subsets, is supercomplete. This result extends results given in [Alstera], [Friedlera], [Frolika], [HohtiPelantb], [Pelanta] and its proof improves that given in [HohtiPelantb].

Countable products of spaces of finite sets

Antonio Avilés (2005)

Fundamenta Mathematicae

We consider the compact spaces σₙ(Γ) of subsets of Γ of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification.

Covariant and contravariant approaches to topology.

Dydak, Jerzy (1997)

International Journal of Mathematics and Mathematical Sciences

Covering dimension of inverse limit of fuzzy spaces

H. Zougdani (1985)

Matematički Vesnik

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.

Covering Properties of Continua and Mappings

Janusz J. Charatonik (2003)

Publications de l'Institut Mathématique

Cozero and Baire maps on products of uniform spaces

Gloria Tashjian (1977)

Fundamenta Mathematicae

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