Complutense University Library

Uniform approximation theorems for real-valued continuous functions


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

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:


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

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.

M.I. Garrido, Approximation Uniforme en Espacios de Funciones Continuas, Publicaciones de1 Departamento de Matematicas, Universidad de Extremadura 24 (Univ. Extremadura, Badajoz, 1990).

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.

L. Gillman and M. Jerison, Rings of Continuous Functions (Springer, Berlin, 1976).

G.J.O. Jameson, Topology and Normal Spaces (Chapman & Hall, London, 1974).

S. Mrowka, On some approximation theorems, Nieuw Arch. Wisk. 16 (1968) 94-1 Il.

R. Narasimhan, Analysis on Real and Complex Manifolds (North-Holland, Amsterdam, 1968).

H. Tie&e, Uber Functionen die anf einer abgeschlossenen Menge steting sind, J. Math. 14.5 (1915) 9-14.

Deposited On:08 Jun 2012 09:04
Last Modified:27 May 2016 14:48

Repository Staff Only: item control page