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The strict topology for $ P$-spaces


Author: Robert F. Wheeler
Journal: Proc. Amer. Math. Soc. 41 (1973), 466-472
MSC: Primary 46E10
DOI: https://doi.org/10.1090/S0002-9939-1973-0341048-9
MathSciNet review: 0341048
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Abstract: A $ P$-space is a completely regular Hausdorff space $ X$ in which every $ {G_\delta }$ is open. It is shown that the generalized strict topologies $ \beta $ and $ {\beta _0}$ coincide on $ {C^\ast }(X)$, and that strong measuretheoretic properties hold; in particular, $ ({C^\ast }(X),\beta )$ is always a strong Mackey space. As an application, an example is constructed of a non-quasi-complete locally convex space in which closed totally bounded sets are compact.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0341048-9
Keywords: $ P$-space, strict topology, strong Mackey space, uniformly $ \tau $-additive, zero-set
Article copyright: © Copyright 1973 American Mathematical Society

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