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

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

Aleksander V. Arhangel'skii (2013)

Commentationes Mathematicae Universitatis Carolinae

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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 ≤ 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

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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.