Absolute Schauder bases for 𝐶(𝑋) with the compact-open topology

Cook, Thurlow A.; Ruckle, William H.

doi:10.1090/S0002-9939-1976-0415283-8

Absolute Schauder bases for $C(X)$ with the compact-open topology
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by Thurlow A. Cook and William H. Ruckle

Proc. Amer. Math. Soc. 59 (1976), 111-114

DOI: https://doi.org/10.1090/S0002-9939-1976-0415283-8

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Abstract:

Let $X$ be a completely regular Hausdorff space and $C(X)$ the space of all real valued continuous functions on $X$. We give $C(X)$ the compact-open topology. The principal result of this paper is: If $C(X)$ is complete and barrelled and has an absolute basis, then $C(X)$ is isomorphic to a countable product of lines.

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Éléments de mathématique

Espaces vectoriels topologiques

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