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Filters, nets and cofinal types
Costantini, Camillo
Priola, Enrico
2001
Abstract
In this paper we investigate functionals relating filters and nets
on a given set X, with special respect to the problem of monotonicity.
In particular, we provide three different functionals $\Psi_{k}\left(k=1,2,3\right)$
from the collection of the filters on X to the class of the nets of
X, such that if $\mathcal{F}\supseteq\mathcal{G}$ then $\Psi_{k}\left(\mathcal{F}\right)$
is a subnet of $\Psi_{k}\left(\mathcal{G}\right)$. We also compare
them with the standard functional N, which fails to be monotone. To
this end, we often use the theory of cofinal types.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
33 (2001)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
C. Costantini, E. Priola, "Filters, nets and cofinal types", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 33 (2001), pp. 1-18.
Languages
en
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