RT Journal Article
T1 Banach-Dieudonné theorem revisited
A1 Bruguera Padró, M. Montserrat
A1 Martín Peinador, Elena
AB We prove that in the character group of an abelian topological group, the topology associated (in a standard way) to the continuous convergence structure is the finest of all those which induce the topology of simple convergence on the corresponding equicontinuous subsets. If the starting group is furthermore metrizable (or even almost metrizable), we obtain that such a topology coincides with the compact-open topology. This result constitutes a generalization of the theorem of Banach-Dieudonné, which is well known in the theory of locally convex spaces. We also characterize completeness, in the class of locally quasi-convex metrizable groups, by means of a property which we have called the quasi-convex compactness property, or briefly qcp (Section 3).
PB Australian Mathematical Society
SN 1446-8107
YR 2003
FD 2003-08
LK https://hdl.handle.net/20.500.14352/49677
UL https://hdl.handle.net/20.500.14352/49677
LA eng
NO D.G.I.C.Y.T.
DS Docta Complutense
RD 10 abr 2025