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S-Barrelled Topological Vector Spaces*

Published online by Cambridge University Press:  20 November 2018

Ray F. Snipes
Ray F. Snipes*
Affiliation:
Department of Mathematics, Bowling Green State University, Bowling GreenOhio 43403
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N. Bourbaki [1] was the first to introduce the class of locally convex topological vector spaces called “espaces tonnelés” or “barrelled spaces.” These spaces have some of the important properties of Banach spaces and Fréchet spaces. Indeed, a generalized Banach-Steinhaus theorem is valid for them, although barrelled spaces are not necessarily metrizable. Extensive accounts of the properties of barrelled locally convex topological vector spaces are found in [5] and [8].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 2 , 01 June 1978 , pp. 221 - 227
Copyright
Copyright © Canadian Mathematical Society 1978

Footnotes

*

Some of these results are contained in the author's Ph.D. thesis written at the University of Virginia under the direction of Professor E. J. McShane.

References

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