Isomorphisms of algebras of smooth functions revisited
Copyright policy )Isomorphisms of algebras of smooth functions revisited
It is proved that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms. It is not required that manifolds are second countable nor paracompact. This solves a problem stated by A. Wienstein. Some related results are discussed as well.
6 pages, minor changes, the final version to appear in Archiv der Mathematik
- Polish Academy of Sciences Poland
- Institute of Mathematics Poland
- Polish Academy of Learning Poland
finite-dimensional manifolds, Mathematics - Differential Geometry, Banach-Stone type theorem, 54C40, 54D60, General Topology (math.GN), Algebraic properties of function spaces in general topology, 58A05, smooth functions, Rings and algebras of continuous, differentiable or analytic functions, Differentiable maps on manifolds, Differential Geometry (math.DG), algebra isomorphism, 46E25; 58A05; 54C40; 54D60, FOS: Mathematics, 46E25, Differentiable manifolds, foundations, Mathematics - General Topology
finite-dimensional manifolds, Mathematics - Differential Geometry, Banach-Stone type theorem, 54C40, 54D60, General Topology (math.GN), Algebraic properties of function spaces in general topology, 58A05, smooth functions, Rings and algebras of continuous, differentiable or analytic functions, Differentiable maps on manifolds, Differential Geometry (math.DG), algebra isomorphism, 46E25; 58A05; 54C40; 54D60, FOS: Mathematics, 46E25, Differentiable manifolds, foundations, Mathematics - General Topology
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