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- W27199506 abstract "Let $X$ be a completely regular Hausdorff space and $E$ a real normed space. We examine the general properties of locally solid topologies on the space $C_b(X,E)$ of all $E$-valued continuous and bounded functions from $X$ into $E$. The mutual relationship between locally solid topologies on $C_b(X,E)$ and $C_b(X)$ $(=C_b(X,Bbb R))$ is considered. In particular, the mutual relationship between strict topologies on $C_b(X)$ and $C_b(X,E)$ is established. It is shown that the strict topology $beta _sigma(X,E)$ (respectively $beta _tau(X,E)$) is the finest $sigma $-Dini topology (respectively Dini topology) on $C_b(X,E)$. A characterization of $sigma $-Dini and Dini topologies on $C_b(X,E)$ in terms of their topological duals is given." @default.
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- W27199506 date "2002-01-01" @default.
- W27199506 modified "2023-09-23" @default.
- W27199506 title "Locally solid topologies on spaces of vector-valued continuous functions" @default.
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