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 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.
@article{bwmeta1.element.bwnjournal-article-fmv150i2p189bwm,
author = {Murray Bell},
title = {A Ramsey theorem for polyadic spaces},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {189-195},
zbl = {0890.54020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i2p189bwm}
}
Bell, Murray. A Ramsey theorem for polyadic spaces. Fundamenta Mathematicae, Tome 149 (1996) pp. 189-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i2p189bwm/
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