  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.
