Geodesic
On Ponomarev-Systems
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 2, pp. 455-467.

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In this paper the relations of mappings and families of subsets are investigated in Ponomarev-systems, and the following results are obtained. (1) $f$ is a sequence-covering (resp. 1-sequence-covering) mapping iff $\mathcal{P}$ is a csf -network (resp. snf -network) of $X$ for a Ponomarev-system $(f, M, X, \mathcal{P})$; (2) $f$ is a sequence-covering (resp. 1-sequence-covering) mapping iff every $\mathcal{P}_n$ is a cs-cover (resp. wsn-cover) of$X$ for a Ponomarev-system $(f, M, X, \{\mathcal{P}_n \})$. As applications of these results, some relations between sequence-covering mappings and 1-sequence-covering mappings are discussed, and a question posed by S. Lin is answered.
In questo lavoro vengono studiate le relazioni fra mappe e famiglie di sottoinsiemi nei sistemi di Ponomarev, e si ottengono i seguenti risultati. (1) $f$ è una "sequence-covering'" (risp. una "1-sequence-covering") mappa se e solo se $\mathcal{P}$ è una csf rete (risp. una snf rete) di $X$ per un sistema di Ponomarev $(f, M, X, \mathcal{P})$; (2) $f$ è una "sequence-covering" (risp. una "1-sequence-covering") mappa se e solo se ogni $\mathcal{P}_n$ è un cs ricoprimento (risp. un wsn ricoprimento) di $X$ per un sistema di Ponomarev $(f, M, X, \{\mathcal{P}_n \})$. Come applicazione di questi risultati vengono discusse alcune relazioni fra "sequence-covering" mappe e "1-sequence-covering" mappe, e si fornisce la risposta a una domanda posta da S. Lin. 
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Ge, Ying; Shou, Lin. On Ponomarev-Systems. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 2, pp. 455-467. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_2_a13/

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