On some generalizations of the Kakutani-stone and stone-Weierstrass theorems

• Autores: Francisco Montalvo Durán , María Isabel Garrido Carballo
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 6, Nº 2-3, 1991, págs. 156-159
• Idioma: inglés
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• Resumen

  • 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.