On some generalizations of the Kakutani-stone and stone-Weierstrass theorems
- Montalvo Durán, Francisco
- Garrido Carballo, María Isabel
ISSN: 0213-8743
Argitalpen urtea: 1991
Alea: 6
Zenbakia: 2-3
Orrialdeak: 156-159
Mota: Artikulua
Beste argitalpen batzuk: Extracta mathematicae
Laburpena
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 Î 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.