# On Ponomarev-Systems

Bollettino dell'Unione Matematica Italiana (2007)

- Volume: 10-B, Issue: 2, page 455-467
- ISSN: 0392-4033

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topGe, Ying, and Shou, Lin. "On Ponomarev-Systems." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 455-467. <http://eudml.org/doc/290400>.

@article{Ge2007,

abstract = {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.},

author = {Ge, Ying, Shou, Lin},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {6},

number = {2},

pages = {455-467},

publisher = {Unione Matematica Italiana},

title = {On Ponomarev-Systems},

url = {http://eudml.org/doc/290400},

volume = {10-B},

year = {2007},

}

TY - JOUR

AU - Ge, Ying

AU - Shou, Lin

TI - On Ponomarev-Systems

JO - Bollettino dell'Unione Matematica Italiana

DA - 2007/6//

PB - Unione Matematica Italiana

VL - 10-B

IS - 2

SP - 455

EP - 467

AB - 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.

LA - eng

UR - http://eudml.org/doc/290400

ER -

## References

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- LIN, S. - YAN, P., Notes on cfp-covers, Comment Math. Univ. Carolinae, 44 (2003), 295- 306. Zbl1100.54021MR2026164
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- SIWIEC, F., Sequence-covering and countably bi-quotient mappings, General Topology Appl., 1 (1971), 143-154. Zbl0218.54016MR288737
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