Algebraic properties of the uniform closure of spaces of continuous functions

For a completely regular space X, C(X) denotes the algebra of all real-valued and continuous functions over X. This paper deals with the problem of knowing when the uniform closure of certain subsets of C(X) has certain algebraic properties. In this context we give an internal condition, ''property A,'' to characterize the linear subspaces whose uniform closure is an inverse-closed subring of C(X).