Cone lattices of upper semicontinuous functions
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- by Gerald Beer PDF
- Proc. Amer. Math. Soc. 86 (1982), 81-84 Request permission
Abstract:
Let $X$ be a compact metric space. A well-known theorem of M. H. Stone states that if $\Omega$ is a vector lattice of continuous functions on $X$ that separates points and contains a nonzero constant function, then the uniform closure of $\Omega$ is $C(X)$. In this article we generalize Stone’s sufficient conditions to the upper semicontinuous functions on $X$ topologized in a natural way.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 81-84
- MSC: Primary 26A15; Secondary 41A65, 54B20
- DOI: https://doi.org/10.1090/S0002-9939-1982-0663871-9
- MathSciNet review: 663871