Abstract
Let E be a non-archimedean normed space over a non-archimedean valued field F. We establish a formula for the distance d(f,W) between a function f ∈ C(X;E), where X is a compact Hausdorff space, and a vector subspace W⊂ C(X;E) which is a module over a subalgebra A ⊂ C(X;F). As a corollary we obtain several approximation results and a non-archimedean analogue of Bishop’s generalization of the Stone-Weierstrass Theorem.
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© 1978 Birkhäuser Verlag Basel
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Prolla, J.B. (1978). Nonarchimedean Function Spaces. In: Butzer, P.L., Szökefalvi-Nagy, B. (eds) Linear Spaces and Approximation / Lineare Räume und Approximation. International Series of Numerical Mathematics / Intermationale Schriftenreihe zur Numberischen Mathematik / Sùrie Internationale D’analyse Numùruque, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7180-8_11
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DOI: https://doi.org/10.1007/978-3-0348-7180-8_11
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-0979-4
Online ISBN: 978-3-0348-7180-8
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