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We study the convergence of a net of subspaces generated by dilations of polynomials in a finite dimensional subspace. As a consequence, we extend the results given by Zó and Cuenya [Advanced Courses of Mathematical Analysis II (Granada, 2004), 193-213, World Scientific, 2007] on a general approach to the problems of best vector-valued approximation on small regions from a finite dimensional subspace of polynomials. 2010 Mathematics Subject Classification. Primary 40A05, 41A10, 41A65.doi:10.33044/revuma.v61n1a02 fatcat:ylitn5pkfzevzdppaaxwokg2je