On isomorphisms of algebras of smooth functions. (English) Zbl 1077.58005

It is shown that for any isomorphism \( T : C^\infty(N)\rightarrow C^\infty(M) \) between the algebras of smooth functions on two Hausdorff smooth manifolds \( M \) and \( N \) (not necessarily second-countable, paracompact or connected), there exists a unique diffeomorphism \( \tau : M\rightarrow N \) such that \( T(f)=f\circ\tau \) for any \( f \in C^\infty(N) \).
The same property holds for isomorphisms between the algebras of smooth functions with compact support.


58C25 Differentiable maps on manifolds
58A05 Differentiable manifolds, foundations
46E25 Rings and algebras of continuous, differentiable or analytic functions
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