Abstract
Let X be a compact Hausdorff space and let D(X) denote the set of all continuous functions f from X into [0,1]. A subset A C D(X) has property V, by deñnition, 1 — φ and φψ belong to A, whenever φ, ψ ∈ A. We prove a theorem of the Stone-Weierstrass type describing the uniform closure of A. Our result generalizes a theorem of R. I. Jewett that had provided a proof for a statement of von Neumann.
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References
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Prolla, J.B. (1990). Uniform Approximation of Continuous Functions with Values in [0,1]. In: Haußmann, W., Jetter, K. (eds) Multivariate Approximation and Interpolation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 94. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5685-0_18
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DOI: https://doi.org/10.1007/978-3-0348-5685-0_18
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5686-7
Online ISBN: 978-3-0348-5685-0
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