Uniform approximation theorems for real-valued continuous functions.

Título inglés	Uniform approximation theorems for real-valued continuous functions.
Título español	Teoremas de aproximación uniforme para funciones reales continuas.
Autor/es	Garrido, M. Isabel ; Montalvo, Francisco
Organización	Dep. Mat. Univ. Extremadura, Badajoz, España
Revista	0213-8743
Publicación	1991, 6 (2-3): 152-155, 10 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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) ¹ 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].
Clasificación UNESCO	120101
Palabras clave español	Teoría de la aproximación ; Espacio de funciones continuas ; Funciones reales ; Anillos de funciones
Código MathReviews	MR1185365
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