On an Elementary Proof of the Stone-Weierstrass Theorem and Some Extensions

In this paper we give an elementary proof of the approximate continuous partition of unit on a compact Hausdorff-space using results developed in [2]. With the aid of this result we give a proof of the well-known localizability theorem for A-modules in C[T,E]. Using a similar but less elementary method we derive a localizability theorem in the case of approximation of elements in C[T,E] by certain sequences of linear operators.