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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equivalence of topologies and Borel fields for countably-Hilbert spaces


Author: Jeremy J. Becnel
Journal: Proc. Amer. Math. Soc. 134 (2006), 581-590
MSC (2000): Primary 57N17; Secondary 60H40
Published electronically: August 12, 2005
MathSciNet review: 2176027
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Abstract: We examine the main topologies--weak, strong, and inductive--placed on the dual of a countably-normed space and the $\sigma$-fields generated by these topologies. In particular, we prove that for certain countably-Hilbert spaces the strong and inductive topologies coincide and the $\sigma$-fields generated by the weak, strong, and inductive topologies are equivalent.


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Additional Information

Jeremy J. Becnel
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: beck@math.lsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08219-5
PII: S 0002-9939(05)08219-5
Received by editor(s): September 2, 2004
Published electronically: August 12, 2005
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.