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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...

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