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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Closed countably generated structures in $ C(X)$


Author: B. Roth
Journal: Trans. Amer. Math. Soc. 177 (1973), 191-197
MSC: Primary 46E25; Secondary 46E05
MathSciNet review: 0317027
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Abstract: Let $ C(X)$ be the space of continuous real or complex valued functions on a compact space X with the sup norm topology. In the present paper, the subalgebras, vector lattices, and vector lattice ideals of $ C(X)$ which are closed and countably generated are characterized.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0317027-9
PII: S 0002-9947(1973)0317027-9
Keywords: Spaces of continuous functions, subalgebras of continuous functions, vector lattices of continuous functions, countably generated subalgebras, countably generated vector lattices, countably generated vector lattice ideals
Article copyright: © Copyright 1973 American Mathematical Society