2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95334It 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 MathematikDifferential GeometryGeneral Topology46E25; 58A05; 54C40; 54D60text