Displaying similar documents to “Observations on spaces with zeroset or regular G δ -diagonals”

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.

H-closed extensions with countable remainder

Daniel K. McNeill (2012)

Commentationes Mathematicae Universitatis Carolinae

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This paper investigates necessary and sufficient conditions for a space to have an H-closed extension with countable remainder. For countable spaces we are able to give two characterizations of those spaces admitting an H-closed extension with countable remainder. The general case is more difficult, however, we arrive at a necessary condition — a generalization of Čech completeness, and several sufficient conditions for a space to have an H-closed extension 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....

Convergence in compacta and linear Lindelöfness

Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (1998)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a compact Hausdorff space with a point x such that X ∖ { x } is linearly Lindelöf. Is then X first countable at x ? What if this is true for every x in X ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when X is, in addition, ω -monolithic. We also prove that if X is compact, Hausdorff, and X ∖ { x } is strongly discretely Lindelöf, for every x in X , then X is first countable. An example of linearly...