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Uniform approximation theorems for real-valued continuous functions.

M. Isabel Garrido, Francisco Montalvo (1991)

Extracta Mathematicae

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...

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