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Strict topology and $ P$-spaces


Authors: Surjit Singh Khurana and Seki Alexander Choo
Journal: Proc. Amer. Math. Soc. 61 (1976), 280-284
MSC: Primary 46E40
DOI: https://doi.org/10.1090/S0002-9939-1976-0425603-6
MathSciNet review: 0425603
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Abstract: For a completely regular Hausdorff space $ X$ and a normed space $ E$, let $ {C_b}(X,\,E)$ be the space of all bounded continuous functions from $ X$ into $ E$ with strict topology $ {\beta _0}$. It is proved that if $ X$ is a $ P$-space, $ ({C_b}(X,E),{\beta _0})$ is Mackey; if, in addition, $ E$ is complete, then $ ({C_b}(X,E),{\beta _0})$ is strongly Mackey.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0425603-6
Keywords: Mackey and strongly Mackey locally convex spaces, strict topology, uniformly tight collection of measures
Article copyright: © Copyright 1976 American Mathematical Society

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