%0 Journal Article
%A Garrido, M. Isabel
%A Montalvo, Francisco
%T Countable covers and uniform closure
%D 1999
%@ 0049-4704
%U https://hdl.handle.net/20.500.14352/58532
%X We present, in a unified way, several results of uniform approximation for real-valued continuous and uniformly continuous functions on a space X . We obtain all of them by applying a general method of proof that involves a certain kind of countable covers of X , the so-called 2-finite covers. For instance, if X  is endowed with the weak uniformity given by a vector lattice F  of real-valued functions on X  containing all the real constant functions then, using that method, we characterize the uniform density of F  only in terms of the family F , thus improving a previous result in this line.
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