Cone Lattices of Upper Semicontinuous Functions
Copyright policy )Cone Lattices of Upper Semicontinuous Functions
Let X X be a compact metric space. A well-known theorem of M. H. Stone states that if Ω \Omega is a vector lattice of continuous functions on X X that separates points and contains a nonzero constant function, then the uniform closure of Ω \Omega is C ( X ) C(X) . In this article we generalize Stone’s sufficient conditions to the upper semicontinuous functions on X X topologized in a natural way.
- California State University Los Angeles United States
- California State University System United States
Function spaces in general topology, lattice of real valued upper semicontinuous functions UC(X) on a compact metric space, Lattices of continuous, differentiable or analytic functions, Hyperspaces in general topology, Stone approximation theorem, Topological lattices, Hausdorff metric, Ordered topological linear spaces, vector lattices, monotone functional
Function spaces in general topology, lattice of real valued upper semicontinuous functions UC(X) on a compact metric space, Lattices of continuous, differentiable or analytic functions, Hyperspaces in general topology, Stone approximation theorem, Topological lattices, Hausdorff metric, Ordered topological linear spaces, vector lattices, monotone functional
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