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Let Ω denote the simplicial complex 
in Rd. For a nonnegative integer p with
let Ω (p)denote the p- skeleton of Ω. Let d = 2 or 3 and suppose that f is a monotone function on Ω (1). We give construction schemes which extend f as a monotone function on Ω, while maintaining smoothness. Our results are related to those of Dahmen, DeVore and Micchelli for the case d = 2 and p = 1.
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