The strict topology for 𝑃-spaces

Wheeler, Robert F.

doi:10.1090/S0002-9939-1973-0341048-9

The strict topology for $P$-spaces
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Proc. Amer. Math. Soc. 41 (1973), 466-472 Request permission

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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