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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bounded continuous functions on a completely regular space


Author: F. Dennis Sentilles
Journal: Trans. Amer. Math. Soc. 168 (1972), 311-336
MSC: Primary 46E10; Secondary 54C35
MathSciNet review: 0295065
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Abstract: Three locally convex topologies on $ C(X)$ are introduced and developed, and in particular shown to coincide with the strict topology on locally compact $ X$ and yield dual spaces consisting of tight, $ \tau $-additive and $ \sigma $-additive functionals respectively for completely regular $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0295065-1
PII: S 0002-9947(1972)0295065-1
Keywords: Locally convex spaces, Mackey topology, strict topology, tight, $ \tau $-additive functionals, $ \sigma $-additive functionals, measure compact, $ D$ spaces
Article copyright: © Copyright 1972 American Mathematical Society