Bruguera Padró, M. Montserrat and Martín Peinador, Elena (2003) BanachDieudonné theorem revisited. Journal of the Australian Mathematical Society , 75 (1). pp. 6983. ISSN 14468107

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Official URL: http://www.austms.org.au/Publ/JAustMS/
Abstract
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 compactopen topology. This result constitutes a generalization of the theorem of BanachDieudonné, which is well known in the theory of locally convex spaces. We also characterize completeness, in the class of locally quasiconvex metrizable groups, by means of a property which we have called the quasiconvex 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:  06 Feb 2014 09:30 
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