H-closed extensions with countable remainder

Daniel K. McNeill

A generalization of Čech-complete spaces and Lindelöf $Σ$ -spaces

Aleksander V. Arhangel'skii (2013)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The class of $s$ -spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf $p$ -spaces, metrizable spaces with the weight $\leq 2^{ω}$ , but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that $s$ -spaces are in a duality with Lindelöf $Σ$ -spaces: $X$ is an $s$ -space if and only if some (every) remainder of $X$ in a compactification is a Lindelöf $Σ$ -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math....

On monotone Lindelöfness of countable spaces

Ronnie Levy, Mikhail Matveev (2008)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A space is monotonically Lindelöf (mL) if one can assign to every open cover $𝒰$ a countable open refinement $r (𝒰)$ so that $r (𝒰)$ refines $r (𝒱)$ whenever $𝒰$ refines $𝒱$ . We show that some countable spaces are not mL, and that, assuming CH, there are countable mL spaces that are not second countable.

Displaying similar documents to “H-closed extensions with countable remainder”

A generalization of Čech-complete spaces and Lindelöf Σ -spaces

On monotone Lindelöfness of countable spaces

A generalization of Čech-complete spaces and Lindelöf $Σ$ -spaces