Abstract: Let Qp denote the field of p-adic numbers. Let S be a zero-dimensional compact Hausdorff space and let C(S; Qp ) be the Banach space of all continuous functions from Sinto Qp equipped with the supremum norm. ln this paper we prove a Weierstrass­Stone type theorem for subsets of C(S; Q,) and apply it to the problem of simultaneous approx.imation and interpolation Ver menos