On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.

Garrido, M. Isabel, and Montalvo, Francisco. "On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.." Extracta Mathematicae 6.2-3 (1991): 156-159. <http://eudml.org/doc/39942>.

@article{Garrido1991,
abstract = {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.},
author = {Garrido, M. Isabel, Montalvo, Francisco},
journal = {Extracta Mathematicae},
keywords = {Teorema de Stone-Weierstrass; Teoría de la aproximación; Espacio de funciones continuas; Anillos de funciones; Stone-Weierstrass theorem; uniform density theorem; uniform approximation; uniform closure},
language = {eng},
number = {2-3},
pages = {156-159},
title = {On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.},
url = {http://eudml.org/doc/39942},
volume = {6},
year = {1991},
}

TY - JOUR
AU - Garrido, M. Isabel
AU - Montalvo, Francisco
TI - On some generalizations of the Kakutani-Stone and Stone-Weierstrass theorems.
JO - Extracta Mathematicae
PY - 1991
VL - 6
IS - 2-3
SP - 156
EP - 159
AB - 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.
LA - eng
KW - Teorema de Stone-Weierstrass; Teoría de la aproximación; Espacio de funciones continuas; Anillos de funciones; Stone-Weierstrass theorem; uniform density theorem; uniform approximation; uniform closure
UR - http://eudml.org/doc/39942
ER -