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

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

2010-01-19

arxiv.org/abs/1001.3231v1

Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques XI, 2 (1969) 207-214

Mathematics

General Topology

Scientific paper

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.

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