Une Structure Uniforme sur un Espace F(E,F)

Nicolas Bouleau (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

Let E be a topological space and F a uniform space. We introduce a new topology (in fact a uniform structure) called the V-congergence on the space of applications from E to F such that C(E,F) is closed for this topology and the restriction of this topology to C(E,F) is equivalent to pointwise convergence. In other words this topology is the coarsest preserving continuity. We give a criterion of convergence for this topology not involving the limit. Among properties preserved are mesurability and alpha-borelianity for a countable ordinal alpha.

Mots clés: continuity; neighborhood; Banach; compact

Domaines: Topologie générale [math.GN]

Nicolas Bouleau. Une Structure Uniforme sur un Espace F(E,F). Cahiers de topologie et géométrie différentielle catégoriques, 1969, XI (2), pp.207-214. ⟨hal-00447814⟩