# Uniform approximation theorems for real-valued continuous functions.

M. Isabel Garrido; Francisco Montalvo

Extracta Mathematicae (1991)

- Volume: 6, Issue: 2-3, page 152-155
- ISSN: 0213-8743

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topGarrido, M. Isabel, and Montalvo, Francisco. "Uniform approximation theorems for real-valued continuous functions.." Extracta Mathematicae 6.2-3 (1991): 152-155. <http://eudml.org/doc/39941>.

@article{Garrido1991,

abstract = {For a completely regular space X, C(X) and C*(X) denote, respectively, the algebra of all real-valued continuous functions and bounded real-valued continuous functions over X. When X is not a pseudocompact space, i.e., if C*(X) ≠ C(X), theorems about uniform density for subsets of C*(X) are not directly translatable to C(X). In [1], Anderson gives a sufficient condition in order for certain rings of C(X) to be uniformly dense, but this condition is not necessary.In this paper we study the uniform closure of a linear subspace of real-valued functions and we obtain, in particular, a necessary and sufficient condition of uniform density in C(X). These results generalize, for the unbounded case, those obtained by Blasco-Moltó for the bounded case [2].},

author = {Garrido, M. Isabel, Montalvo, Francisco},

journal = {Extracta Mathematicae},

keywords = {Teoría de la aproximación; Espacio de funciones continuas; Funciones reales; Anillos de funciones; uniform continuity; uniform density},

language = {eng},

number = {2-3},

pages = {152-155},

title = {Uniform approximation theorems for real-valued continuous functions.},

url = {http://eudml.org/doc/39941},

volume = {6},

year = {1991},

}

TY - JOUR

AU - Garrido, M. Isabel

AU - Montalvo, Francisco

TI - Uniform approximation theorems for real-valued continuous functions.

JO - Extracta Mathematicae

PY - 1991

VL - 6

IS - 2-3

SP - 152

EP - 155

AB - For a completely regular space X, C(X) and C*(X) denote, respectively, the algebra of all real-valued continuous functions and bounded real-valued continuous functions over X. When X is not a pseudocompact space, i.e., if C*(X) ≠ C(X), theorems about uniform density for subsets of C*(X) are not directly translatable to C(X). In [1], Anderson gives a sufficient condition in order for certain rings of C(X) to be uniformly dense, but this condition is not necessary.In this paper we study the uniform closure of a linear subspace of real-valued functions and we obtain, in particular, a necessary and sufficient condition of uniform density in C(X). These results generalize, for the unbounded case, those obtained by Blasco-Moltó for the bounded case [2].

LA - eng

KW - Teoría de la aproximación; Espacio de funciones continuas; Funciones reales; Anillos de funciones; uniform continuity; uniform density

UR - http://eudml.org/doc/39941

ER -

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