Uniform approximation theorems for real-valued continuous functions.

Garrido, 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 -