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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4221

Title: Filters, nets and cofinal types
Authors: Costantini, Camillo
Priola, Enrico
Keywords: filter
directed set
net
subnet
convergent function
cofinal type
monotone functional
ponet
Issue Date: 2001
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: 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.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
33 (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.
URI: http://hdl.handle.net/10077/4221
ISSN: 0049-4704
MS Classification: 03EO5
06A07
54A20
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.33 (2001)

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