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Tightness and π-character in centered spaces

Murray Bell — 1999

Colloquium Mathematicae

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 centered...

On character and chain conditions in images of products

Murray Bell — 1998

Fundamenta Mathematicae

A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property R λ ' which we show is satisfied by all ξ-adic spaces. Whereas Property R λ ' is productive, we show that a weaker (but more natural) Property R λ is not productive. Polyadic...

A Ramsey theorem for polyadic spaces

Murray Bell — 1996

Fundamenta Mathematicae

A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that ( α κ ) ω is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage....

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