Uniform algebras invariant under every homeomorphism
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- by Alexander J. Izzo PDF
- Trans. Amer. Math. Soc. 367 (2015), 231-250 Request permission
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.References
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Additional Information
- Alexander J. Izzo
- Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
- MR Author ID: 307587
- Email: aizzo@math.bgsu.edu
- 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.
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3271259
Dedicated: Dedicated to James Munkres on the occasion of his 80th birthday