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

M. Isabel Garrido; Francisco Montalvo

Extracta Mathematicae (1991)

- Volume: 6, Issue: 2-3, page 156-159
- ISSN: 0213-8743

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topGarrido, 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 -