A RAFU linear space uniformly dense in C [a, b]

In this paper we prove that a RAFU (radical functions) linear space, ∁, is uniformly dense in C [a, b] by means of a S-separation condition of certain subsets of [a, b] due to Blasco-Moltó. This linear space is not a lattice or an algebra. Given an arbitrary function f 2 C [a, b] we will obtain easily the sequence (Cn)n of ∁ that converges uniformly to f and we will show the degree of uniform approximation to f with (Cn)n