Geodesic
A Ramsey theorem for polyadic spaces
Fundamenta Mathematicae, Tome 150 (1996) no. 2, pp. 189-195 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $(ακ)^ω$ 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. Another consequence is that the property of being polyadic is not a regular closed hereditary property.
DOI : 10.4064/fm-150-2-189-195
Keywords: polyadic, regular closed, uniform Eberlein, hyperspace

M. Bell 1

1 
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M. Bell. A Ramsey theorem for polyadic spaces. Fundamenta Mathematicae, Tome 150 (1996) no. 2, pp. 189-195. doi: 10.4064/fm-150-2-189-195

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