Uniform approximation theorems for real-valued continuous functions



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Garrido, 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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Official URL: http://www.sciencedirect.com/science/article/pii/0166864192900544


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
Deposited On:08 Jun 2012 09:04
Last Modified:12 Dec 2018 15:13

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