Strict topology and 𝑃-spaces

Khurana, Surjit Singh; Choo, Seki Alexander

doi:10.1090/S0002-9939-1976-0425603-6

Strict topology and $P$-spaces
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by Surjit Singh Khurana and Seki Alexander Choo PDF

Proc. Amer. Math. Soc. 61 (1976), 280-284 Request permission

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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