On the coarsest topology preserving continuity

Details On the coarsest topology preserving continuity On the coarsest topology preserving continuity

2006-10-11

arxiv.org/abs/math/0610373v1

Mathematics

General Topology

14p

Scientific paper

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.

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