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Countable covers and uniform closure
Montalvo, F.
Garrido, L.
1999
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1999) suppl.
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.
Languages
en
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