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On isomorphisms of algebras of smooth functions
Author(s):
Janez
Mrcun
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3109-3113.
MSC (2000):
Primary 58A05;
Secondary 46E25
Posted:
April 8, 2005
MathSciNet review:
2159792
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Abstract:
We show that for any smooth Hausdorff manifolds  and  , which are not necessarily second-countable, paracompact or connected, any isomorphism from the algebra of smooth (real or complex) functions on  to the algebra of smooth functions on  is given by composition with a unique diffeomorphism from  to  . An analogous result holds true for isomorphisms of algebras of smooth functions with compact support.
References:
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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:
10.1090/S0002-9939-05-07979-7
PII:
S 0002-9939(05)07979-7
Received by editor(s):
May 18, 2004
Posted:
April 8, 2005
Additional Notes:
This work was supported in part by the Slovenian Ministry of Science.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2005,
American Mathematical Society
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