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Countable covers and uniform closure

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Garrido, M. Isabel and Montalvo, Francisco (1999) Countable covers and uniform closure. Rendiconti dell'Istituto di Matematica dell'Università di Trieste., 30 (suplem). pp. 91-102. ISSN 0049-4704

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Official URL: http://rendiconti.dmi.units.it/node/4/4200


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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.


Item Type:Article
Additional Information:

Proceedings of the "I Congreso Hispano-Italiano de Topología General y sus Aplicaciones",Gandia, June 19–21, 1997

Uncontrolled Keywords:uniform approximation, uniform closure and 2-unite cover
Subjects:Sciences > Mathematics > Topology
ID Code:21630
Deposited On:31 May 2013 14:51
Last Modified:12 Dec 2018 15:13

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