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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On isomorphisms of algebras of smooth functions


Author: Janez Mrcun
Journal: Proc. Amer. Math. Soc. 133 (2005), 3109-3113
MSC (2000): Primary 58A05; Secondary 46E25
Published electronically: April 8, 2005
MathSciNet review: 2159792
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that for any smooth Hausdorff manifolds $M$ and $N$, which are not necessarily second-countable, paracompact or connected, any isomorphism from the algebra of smooth (real or complex) functions on $N$ to the algebra of smooth functions on $M$ is given by composition with a unique diffeomorphism from $M$ to $N$. An analogous result holds true for isomorphisms of algebras of smooth functions with compact support.


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Additional Information

Janez Mrcun
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
Email: janez.mrcun@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07979-7
PII: S 0002-9939(05)07979-7
Received by editor(s): May 18, 2004
Published electronically: April 8, 2005
Additional Notes: This work was supported in part by the Slovenian Ministry of Science.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society