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Universal uniform Eberlein compact spaces


Author: M. Bell
Journal: Proc. Amer. Math. Soc. 128 (2000), 2191-2197
MSC (1991): Primary 54D30, 54A25; Secondary 54C20, 54H10
DOI: https://doi.org/10.1090/S0002-9939-00-05403-4
Published electronically: February 25, 2000
MathSciNet review: 1676311
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Abstract: A universal space is one that continuously maps onto all others of its own kind and weight. We investigate when a universal Uniform Eberlein compact space exists for weight $\kappa$. If $\kappa = 2^{<\kappa}$, then they exist whereas otherwise, in many cases including $\kappa = \omega _1$, it is consistent that they do not exist. This answers (for many $\kappa$ and consistently for all $\kappa$) a question of Benyamini, Rudin and Wage of 1977.


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Additional Information

M. Bell
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Email: mbell@cc.umanitoba.ca

DOI: https://doi.org/10.1090/S0002-9939-00-05403-4
Keywords: Compact space, Uniform Eberlein, universal, boolean algebra, graph
Received by editor(s): May 5, 1998
Received by editor(s) in revised form: September 6, 1998
Published electronically: February 25, 2000
Additional Notes: The author would like to thank NSERC of Canada for support for this research.
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society

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