Uniform approximation theorems for real-valued continuous functions
- Garrido Carballo, María Isabel
- Montalvo Durán, Francisco
ISSN: 0213-8743
Argitalpen urtea: 1991
Alea: 6
Zenbakia: 2-3
Orrialdeak: 152-155
Mota: Artikulua
Beste argitalpen batzuk: Extracta mathematicae
Laburpena
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].