A Ramsey theorem for polyadic spaces

Volume 150 / 1996

M. Bell Fundamenta Mathematicae 150 (1996), 189-195 DOI: 10.4064/fm-150-2-189-195


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.


  • M. Bell

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