On character and chain conditions in images of products

Bell, Murray

Bell, Murray

Fundamenta Mathematicae, Tome 158 (1998), p. 41-49 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 1998-01-01

Zbl 0920.54023

EUDML-ID : urn:eudml:doc:212301

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     author = {Murray Bell},
     title = {On character and chain conditions in images of products},
     journal = {Fundamenta Mathematicae},
     volume = {158},
     year = {1998},
     pages = {41-49},
     zbl = {0920.54023},
     language = {en},
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Bell, Murray. On character and chain conditions in images of products. Fundamenta Mathematicae, Tome 158 (1998) pp. 41-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv158i1p41bwm/

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