Banach-Dieudonné theorem revisited



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Bruguera Padró, M. Montserrat and Martín Peinador, Elena (2003) Banach-Dieudonné theorem revisited. Journal of the Australian Mathematical Society , 75 (1). pp. 69-83. ISSN 1446-8107

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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).

Item Type:Article
Uncontrolled Keywords:Complete; Metrizable group; Continuous convergence structure; Equicontinuous weak* topology
Subjects:Sciences > Mathematics > Topology
ID Code:12708
Deposited On:13 May 2011 11:00
Last Modified:12 Dec 2018 15:13

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