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
Official URL: http://www.austms.org.au/Publ/JAustMS/
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).
|Uncontrolled Keywords:||Complete; Metrizable group; Continuous convergence structure; Equicontinuous weak* topology|
|Subjects:||Sciences > Mathematics > Topology|
|Deposited On:||13 May 2011 13:00|
|Last Modified:||13 May 2011 13:00|
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