Topology Atlas Conference Abstracts, Document caab-72.htm

The 1996 Joint
Spring Topology Conference
Southeast Dynamical Systems Conference
March 7-9, 1996
Ball State University
Muncie, Indiana
A Ramsey Theorem for Polyadic Spaces


Murray G. Bell
( University of Manitoba )

A polyadic space is a Hausdorff continuous image of some power of the 1-point compactification of a discrete space. We prove a Ramsey-like 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.

Received by the editors: January 11, 1996.

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