The strict topology for $P$-spaces
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- by Robert F. Wheeler
- Proc. Amer. Math. Soc. 41 (1973), 466-472
- DOI: https://doi.org/10.1090/S0002-9939-1973-0341048-9
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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.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- 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