Biström, P.Jaramillo Aguado, Jesús Ángel2023-06-202023-06-2019940025-5521https://hdl.handle.net/20.500.14352/57614In this article it is proved that any set in a real Banach space on which the C-infinity-functions are bounded, is relatively compact. In particular, for any real Banach space E, a sequence (x(n)) convergences to x in E if and only if f(x(n)) --> S(x) for all f is an element of C-infinity(E).engjournal articlehttp://www.digizeitschriften.derestricted access517.98C1-bounding setscompactnessAnálisis funcional y teoría de operadores