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Proceedings of the American Mathematical Society

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

 
 

 

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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Keywords: Mackey and strongly Mackey locally convex spaces, strict topology, uniformly tight collection of measures
Article copyright: © Copyright 1976 American Mathematical Society