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Title: Countable covers and uniform closure
Authors: Montalvo, F.
Garrido, L.
Keywords: uniform approximationuniform closure and 2-finite cover
Issue Date: 1999
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: I. Garrido and F. Montalvo, "Countable covers and uniform closure", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1999) suppl., pp. 91-102.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1999) suppl.
Abstract: In this paper we present, in a unified way, several results af uniform approximation for real-valued continuous and uniformly continuous functions an a space X. We obtain all of them by applying a general method af proof that involves certain kind of cauntable covers af X, the so-called 2-finite covers. For instance, if X is endowed with the weak uniformity given by a vector lattice $\mathfrak{F}$ of real-valued functions an X containing all the real constant functions then, using that method, we characterize the uniform density of $\mathfrak{F}$ only in terms of the family $\mathfrak{F}$, improving a previous result in this line.
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.30 (1999) s.

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