Biblioteca de la Universidad Complutense de Madrid

Uniform approximation theorems for real-valued continuous functions

Impacto

Garrido, M. Isabel y 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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URL Oficial: http://www.sciencedirect.com/science/article/pii/0166864192900544




Resumen

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.


Tipo de documento:Artículo
Palabras clave:Lebesgue chain condition
Materias:Ciencias > Matemáticas > Topología
Código ID:15541
Referencias:

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.

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Última Modificación:27 May 2016 14:48

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