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On character and chain conditions in images of products

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Bell M. G.

Fundamenta Mathematicae

1998

tom 158

nr 1

41-49

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 spaces are shown to satisfy a stronger chain condition called Property $R_λ''$. We use Property $R_λ'$ to show that not all compact, monolithic, scattered spaces are ξ-adic, thus answering a question of Chertanov's.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Bell M. G.

1 1998

Wyniki wyszukiwania

On character and chain conditions in images of products