Uniform approximation theorems for real-valued continuous functions

Abstract

From the introduction: "We study the uniform closure of a linear subspace of real-valued functions and we obtain, in particular, a necessary and sufficient condition for uniform density in C(X). These results generalize, for the unbounded case, those obtained by J. L. Blasco and A. Moltó [Ann. Mat. Pura Appl. (4) 134 (1983), 233–239 for the bounded case. The approximation technique used by them (essentially the same one used in papers by Tietze, S. Mrówka and G. J. O. Jameson) is also the starting point for us.''