A Ramsey Theorem for Polyadic Spaces
by
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.

Date received: January 11, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caab-72.