Displaying similar documents to “On Eberlein compactifications of metrizable spaces”

Resolving a question of Arkhangel'skiĭ's

Michael G. Charalambous (2006)

Fundamenta Mathematicae

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We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.

More about spaces with a small diagonal

Alan Dow, Oleg Pavlov (2006)

Fundamenta Mathematicae

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Hušek defines a space X to have a small diagonal if each uncountable subset of X² disjoint from the diagonal has an uncountable subset whose closure is disjoint from the diagonal. Hušek proved that a compact space of weight ω₁ which has a small diagonal will be metrizable, but it remains an open problem to determine if the weight restriction is necessary. It has been shown to be consistent that each compact space with a small diagonal is metrizable; in particular, Juhász and Szentmiklóssy...

Images of B(k)

R. Freiwald (1978)

Fundamenta Mathematicae

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I-weight of compact and locally compact LOTS

Brad Bailey (2007)

Commentationes Mathematicae Universitatis Carolinae

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Ram’ırez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [, Topology Proc. (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of the space and the i-weight of open sets or the local i-weight. For locally compact LOTS we find a necessary and sufficient condition...