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Uniform algebras invariant under every homeomorphism


Author: Alexander J. Izzo
Journal: Trans. Amer. Math. Soc. 367 (2015), 231-250
MSC (2010): Primary 46J10; Secondary 22F50, 32A65, 54C35, 54H15, 57P99, 57S99
DOI: https://doi.org/10.1090/S0002-9947-2014-06023-6
Published electronically: July 16, 2014
MathSciNet review: 3271259
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Abstract: For a broad class of spaces $ X$, we show that $ C(X)$ is the only uniform algebra on $ X$ that is invariant under every self-homeomorphism of $ X$. This class of spaces contains the manifolds-with-boundary and the finite simplicial complexes. We also give examples showing that the result fails for CW complexes.


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Additional Information

Alexander J. Izzo
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: aizzo@math.bgsu.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06023-6
Received by editor(s): May 14, 2012
Received by editor(s) in revised form: November 14, 2012
Published electronically: July 16, 2014
Additional Notes: This paper was presented to the American Mathematical Society in preliminary form on April 9, 2011 under the title Function algebras invariant under every self-homeomorphism.
Dedicated: Dedicated to James Munkres on the occasion of his 80th birthday
Article copyright: © Copyright 2014 American Mathematical Society