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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Cone lattices of upper semicontinuous functions


Author: Gerald Beer
Journal: Proc. Amer. Math. Soc. 86 (1982), 81-84
MSC: Primary 26A15; Secondary 41A65, 54B20
MathSciNet review: 663871
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0663871-9
PII: S 0002-9939(1982)0663871-9
Keywords: Semicontinuous function, Stone Approximation Theorem, Hausdorff metric, monotone functional
Article copyright: © Copyright 1982 American Mathematical Society