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In this paper we present a Stone-Weierstrass type result in the context of continuous interval-valued functions defined on a compact Hausdorff space. We also provide a Jackson type approximation result involving the modulus of continuity of interval-valued functions based on the  gH -difference of intervals. Finally we show how an interval-valued continuous function can be approximated using interval neural networks. All the proofs are constructive.

Constructive Approximation of Continuous Interval-Valued Functions