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The essential closure of $ C(X)$


Author: Marlow Anderson
Journal: Proc. Amer. Math. Soc. 76 (1979), 8-10
MSC: Primary 06F15; Secondary 54C40
DOI: https://doi.org/10.1090/S0002-9939-1979-0534378-4
MathSciNet review: 534378
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Abstract: Each archimedean l-group admits a unique essential closure, which is the l-group of continuous almost finite real-valued functions on some Stonean space; thus the l-group $ C(X)$ of real-valued continuous functions on a topological space X admits such an essential closure. In this note we will construct a natural embedding of $ C(X)$ into its essential closure, making explicit the topological relationship between X and the appropriate Stonean space.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0534378-4
Article copyright: © Copyright 1979 American Mathematical Society

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