Abstract: Let A be a subalgebra of C(T,IR), where T is a compact Hausdorff space. It is well known that the uniform closure of A is proximinal in C(T,IR) equipped with the sup-norm. In this paper we show that the uniform closure of NA :=1(f€E A; É > 0), say V, is proximinal too. Moreover, for any bounded non-empty subset BC C(T,IR), the set ocent(B;vV of relative Chebyshev centers of Bí(with respect to V) is non-empty. The proof relies on a generalization of Bernstein's Theorem on approximation of a positive continuous function f£ on [0,1] by its Bernstein polynomials BR (f) Ver menos