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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Separability in the strict and substrict topologies


Author: W. H. Summers
Journal: Proc. Amer. Math. Soc. 35 (1972), 507-514
MSC: Primary 46E10; Secondary 54E35
MathSciNet review: 0303272
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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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DOI: https://doi.org/10.1090/S0002-9939-1972-0303272-X
Keywords: Strict topology, separable space, tight functional, $ \tau $-smooth functional, submetrizable space
Article copyright: © Copyright 1972 American Mathematical Society