Publication: Countable covers and uniform closure
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Publication Date
1999
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Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Abstract
We present, in a unified way, several results of uniform approximation for real-valued continuous and uniformly continuous functions on a space X . We obtain all of them by applying a general method of proof that involves a certain kind of countable covers of X , the so-called 2-finite covers. For instance, if X is endowed with the weak uniformity given by a vector lattice F of real-valued functions on X containing all the real constant functions then, using that method, we characterize the uniform density of F only in terms of the family F , thus improving a previous result in this line.
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Proceedings of the "I Congreso Hispano-Italiano de Topología General y sus Aplicaciones",Gandia, June 19–21, 1997
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R. Engelking, General topology, PWN-Polish Scientific, Warsaw, 1977.
I. Garrido, Aproximación uniforme en espacios de funciones continuas, Ph.D. thesis, Dpto. Matemáticas, Uex, 24, 1990.
I. Garrido and F. Montalvo, Uniform approximation theorems for real-valued continuous functions, Topology Appl. 45 (1992), 145-155.
I. Garrido and F. Montalvo, Algebraic properties of the uniform closure on spaces of continuous functions, Papers on General Topology and Applications, Ann. New York Acad. Sci., vol. 788, 1996, pp. 101-107.
I. Garrido and F. Montalvo, Some density results for uniformly continuous functions, Topology Appl. 77 (1997), 131-137.