This is an announcement for the paper "About countably-normed spaces" by Jeremy J. Becnel.
Abstract: Here we present an overview of countably normed spaces. In particular, we discuss the main topologies---weak, strong, inductive, and Mackey---placed on the dual of a countably normed spaces and discuss the sigma fields generated by these topologies. In particlar, we show that the strong, inductive, and Mackey topologies are equivalent under reasonable conditions. Also we show that all four topologies induce the same Borel field under certain conditions. The purpose in mind is to provide the background material for many of the results used in White Noise Analysis.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46A11
Remarks: 23 pages, 0 figures, Background material for White Noise Analysis
The source file(s), NuclearSpace.bbl: 1198 bytes, NuclearSpace.tex: 1472 bytes, borel.tex: 5271 bytes, cns.tex: 16479 bytes, compare.tex: 6600 bytes, conclusion.tex: 4430 bytes, inductive.tex: 6567 bytes, nuclear.sty: 4578 bytes, strong.tex: 17400 bytes, tvs.tex: 14418 bytes, weak.tex: 3536 bytes, is(are) stored in gzipped form as 0407200.tar.gz with size 23kb. The corresponding postcript file has gzipped size 103kb.
Submitted from: beck@math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0407200
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http://arXiv.org/abs/math.FA/0407200
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