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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.

References [Enhancements On Off] (What's this?)

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Keywords: Semicontinuous function, Stone Approximation Theorem, Hausdorff metric, monotone functional
Article copyright: © Copyright 1982 American Mathematical Society

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