
A Ramsey Theorem for Polyadic Spaces
by
Murray G. Bell

A polyadic space is a Hausdorff continuous image of some power of the 1point compactification of a discrete space. We prove a Ramseylike property for polyadic spaces which for Boolean spaces can be stated as: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that ($\alpha$$\kappa$)^{$\omega$} is not a Universal preimage for Uniform Eberleins of weight at most $\kappa$, thus answering a question of Y. Benayamini, M. Rudin and M. Wage. Another consequence is that the property of being polyadic is not a regular closed hereditary property.