Geodesic
On character and chain conditions in images of products
Fundamenta Mathematicae, Tome 158 (1998) no. 1, pp. 41-49

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-158-1-41-49
Keywords: compact, scattered, products, chain condition, ordinals

M. Bell 1

1 
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M. Bell. On character and chain conditions in images of products. Fundamenta Mathematicae, Tome 158 (1998) no. 1, pp. 41-49. doi: 10.4064/fm-158-1-41-49

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