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Uniform approximation theorems for real-valued continuous functions

  • Autores: María Isabel Garrido Carballo Árbol académico, Francisco Montalvo Durán Árbol académico
  • Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 6, Nº 2-3, 1991, págs. 152-155
  • Idioma: inglés
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  • Resumen
    • 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].


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