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Dieudonné property. (English) Zbl 1033.46022

Let \(X_0\) be a locally compact Hausdorff space, \(C_0(X_0)\) the space of all scalar-valued bounded continuous functions on \(X_0\) vanishing at infinity, and \(X\) the one-point compactification of \(X_0\). In the present paper, the Dieudonné property of \(C_0(X_0)\) is derived from the Dieudonné property of \(C(X)\). This result is extended to the space \(C_0(X_0,E)\), \(E\) being a Banach space.

MSC:

46E10 Topological linear spaces of continuous, differentiable or analytic functions
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
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References:

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