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 uniform density of algebras and lattices of C*(K), can be characterized.
@article{urn:eudml:doc:39942,
title = {On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.},
journal = {Extracta Mathematicae},
volume = {6},
year = {1991},
pages = {156-159},
mrnumber = {MR1185366},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39942}
}
Garrido, M. Isabel; Montalvo, Francisco. On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.. Extracta Mathematicae, Tome 6 (1991) pp. 156-159. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39942/