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Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

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A new cardinality bound on homogeneous spaces via the Erdös-Rado theorem
by
Nathan Carlson
University of Arizona
Coauthors: Guit-Jan Ridderbos, Vrije Universiteit, The Netherlands

In 1978 E. van Douwen proved that if X is a power homogeneous Hausdorff space then |X| ≤ 2pw(X). Given the bound 2w(X) for general Hausdorff spaces X, this result demonstrated that well-known cardinality bounds can be improved in the presence of homogeneity. Using the Erdös-Rado Theorem, we give a substantial improvement on the van Douwen bound: if X is power homogeneous and Hausdorff, then |X| ≤ 2c(X)pc(X). One may compare this with the cardinality bound 2c(X)c(X), proved by Hajnal and Juhász, for an arbitrary Hausdorff space X. Our result appears to be the first application of a partition relation in the context of homogeneity.

Date received: January 9, 2008

Copyright © 2008 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 # cawk-16.