2003/09/30 by Janez Mrcun
Mathematics · #math.DG #math.FA #msc:58A05 #msc:46E25
published as Proc. Amer. Math. Soc. 133 (2005) 3109-3113 · 5 pages
arxiv created 2005/07/23 · arxiv updated 2009/12/01
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.