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


Authors: Thurlow A. Cook and William H. Ruckle
Journal: Proc. Amer. Math. Soc. 59 (1976), 111-114
MSC: Primary 46E10
DOI: https://doi.org/10.1090/S0002-9939-1976-0415283-8
MathSciNet review: 0415283
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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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DOI: https://doi.org/10.1090/S0002-9939-1976-0415283-8
Article copyright: © Copyright 1976 American Mathematical Society