Displaying similar documents to “Reflecting topological properties in continuous images”

Sequential compactness vs. countable compactness

Angelo Bella, Peter Nyikos (2010)

Colloquium Mathematicae

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The general question of when a countably compact topological space is sequentially compact, or has a nontrivial convergent sequence, is studied from the viewpoint of basic cardinal invariants and small uncountable cardinals. It is shown that the small uncountable cardinal 𝔥 is both the least cardinality and the least net weight of a countably compact space that is not sequentially compact, and that it is also the least hereditary Lindelöf degree in most published models. Similar results,...

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...

Tightness and π-character in centered spaces

Murray Bell (1999)

Colloquium Mathematicae

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We continue an investigation into centered spaces, a generalization of dyadic spaces. The presence of large Cantor cubes in centered spaces is deduced from tightness considerations. It follows that for centered spaces X, πχ(X) = t(X), and if X has uncountable tightness, then t(X) = supκ : 2 κ ⊂ X. The relationships between 9 popular cardinal functions for the class of centered spaces are justified. An example is constructed which shows, unlike the dyadic and polyadic properties, that the...

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...