Construcción de la topología de la convergencia débil en el espacio de Hilbert

Abstract

Weak sequential convergence defines a topology by the requirement that a set O is open if xn⇀x and x∈O implies almost every xn∈O. This topology, Tc, is considered for a real Hilbert (separable) space. A form for the neighborhoods of the origin is given and Tc is compared with the weak topology. Tc is the finest topology that induces the same topology in bounded sets as the weak topology. Tc is an S-topology for S the set of pre-compact sets. The relation with other S-topologies is also given