On the coarsest topology preserving continuity

Nicolas Bouleau (1)

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

We study a topology on a space of functions, called sticking topology, with the property to be the weakest among the topologies preserving continuity. In suitable frameworks, this topology preserves borelianity, local integrability, right continuity and other properties. It is coarser than the locally uniform convergence and it allows the presence of gliding humps as we show on examples. We prove relative compactness criteria for this topology and we consider some extensions.

Mots clés: topology; continuity; cadlag; relative compactness; gliding hump

Domaines: Topologie générale [math.GN]

Nicolas Bouleau. On the coarsest topology preserving continuity. 2006. ⟨hal-00105642⟩