Bounded continuous functions on a completely regular space

Sentilles, F. Dennis

doi:10.1090/S0002-9947-1972-0295065-1

Bounded continuous functions on a completely regular space
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Trans. Amer. Math. Soc. 168 (1972), 311-336 Request permission

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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