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Uniform approximation theorems for real-valued continuous functions

Garrido Carballo, M. Isabel and Montalvo, Francisco (1992) Uniform approximation theorems for real-valued continuous functions. Topology and its Applications, 45 (2). pp. 145-155. ISSN 0166-8641

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Abstract

For a topological space X, F(X) denotes the algebra of real-valued functions over X and C(X) the subalgebra of all functions in F(X) which are continuous. In this paper we characterize the uniformly dense linear subspaces of C(X) by means of the so-called "Lebesgue chain condition". This condition is a generalization to the unbounded case of the S-separation by Blasco and Molto for the bounded case. Through the Lebesgue chain condition we also characterize the linear subspaces of F(X) whose uniform closure is closed under composition with uniformly continuous functions.

Item Type:Article
Uncontrolled Keywords:Lebesgue chain condition
Subjects:Sciences > Mathematics > Topology
ID Code:15541
References:

F.W. Anderson, Approximation in systems of real-valued continuous functions, Trans. Amer. Math. Sot. 103 (1962) 249-271.

J.L. Blasco and A. Molto, On the uniform closure of a linear space of bounded real-valued functions, Ann. Mat. Pura Appl. (4) 134 (1983) 233-239.

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M.I. Garrido and F. Montalvo, S-separation de conjuntos de Lebesgue y condition de cadena, in: Actas de XIV Jornadas Hispano-Lusas de Matematicas (Univ. de La Laguna, Tenerife, 1990) 621-624.

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Last Modified:06 Feb 2014 10:26

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