%0 Journal Article
%A Garrido, M. Isabel
%A Montalvo, Francisco
%T On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems
%D 1991
%@ 0213-8743
%U https://hdl.handle.net/20.500.14352/58549
%X From the introduction: "For a completely regular space X , C ∗ (X)  denotes the algebra of all bounded real-valued continuous functions over X . We consider the topology of uniform convergence over C ∗ (X) . "In this paper we carry out a systematic study of uniform approximation for algebras and lattices of C ∗ (X) . If F  is an algebra or lattice (vector lattice, affine lattice,… ) we characterize its uniform closure and we give necessary and sufficient conditions for uniform density in C ∗ (X) . For our purposes we identify the rings C ∗ (X)  and C(βX)  (βX  is the Stone-Čech compactification of X ). In this way, we generalize the classical results in the compact case and also obtain the generalizations by Hewitt and Blasco
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