On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.
M. Isabel Garrido, Francisco Montalvo (1991)
Extracta Mathematicae
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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). When K is a compact space, the Stone-Weierstrass and Kakutani-Stone theorems provide necessary and sufficient conditions under which a function f ∈ C*(K) can be uniformly approximated by members of an algebra, lattice or vector lattice of C*(K). In this way, the uniform closure and, in particular, the...