On isomorphisms of algebras of smooth functions

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.