On isomorphisms of algebras of smooth functions
Differential Geometry
2007-05-23 v4 Functional Analysis
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.
Cite
@article{arxiv.math/0309179,
title = {On isomorphisms of algebras of smooth functions},
author = {Janez Mrcun},
journal= {arXiv preprint arXiv:math/0309179},
year = {2007}
}
Comments
5 pages