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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
DOI: https://doi.org/10.1090/S0002-9947-1972-0295065-1
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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Keywords: Locally convex spaces, Mackey topology, strict topology, tight, <IMG WIDTH="17" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\tau$">-additive functionals, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img9.gif" ALT="$\sigma$">-additive functionals, measure compact, <IMG WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$D$"> spaces
Article copyright: © Copyright 1972 American Mathematical Society