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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 | 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. | 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. |
Type: | Article | URI: | http://hdl.handle.net/10077/4221 | ISSN: | 0049-4704 |
Appears in Collections: | Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.33 (2001) |
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CostantiniPriolaRendMat33.pdf | 224.36 kB | Adobe PDF | ![]() View/Open |
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