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On isomorphisms of algebras of smooth functions

Janez Mrcun
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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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Janez Mrcun. 2005-07-23. On isomorphisms of algebras of smooth functions. https://arxiv.org/abs/math/0309179

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