Separability in the strict and substrict topologies

Summers, W. H.

doi:10.1090/S0002-9939-1972-0303272-X

Separability in the strict and substrict topologies
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Proc. Amer. Math. Soc. 35 (1972), 507-514 Request permission

Abstract:

Let X denote a locally compact Hausdorff space, ${C_b}(X)$ the space of all bounded continuous complex valued functions on X, and $\beta$ the strict topology for ${C_b}(X)$. The separability of $({C_b}(X),\beta )$ is characterized in terms of X, albeit in a more general context. This result provides a negative answer to a conjecture made by Todd, contains the classical separability theorems for continuous function spaces, and relates to the concepts of $\tau$-smooth and tight functionals.

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