On Ponomarev-Systems

Ying Ge; Lin Shou

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 455-467
  • ISSN: 0392-4041

Abstract

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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 𝒫 is a csf -network (resp. snf -network) of X for a Ponomarev-system ( f , M , X , 𝒫 ) ; (2) f is a sequence-covering (resp. 1-sequence-covering) mapping iff every 𝒫 n is a cs-cover (resp. wsn-cover) of X for a Ponomarev-system ( f , M , X , { 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.

How to cite

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Ge, 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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  2. GE, Y., Mappings in Ponomarev-Systems, Topology Proc., 29 (2005), 141-153. Zbl1085.54018MR2182923
  3. GRUENHAGE, G. - MICHAEL, E. - TANAKA, Y., Spaces determined by point-countable covers, Pacific J. Math., 113 (1984), 303-332. Zbl0561.54016MR749538
  4. GUTHRIE, J. A., A characterization of ℵ 0 -spaces, General Topology Appl., 1 (1971), 105-110. Zbl0216.19103MR288726
  5. LIN, S., A note on the Arens' spaces and sequential fan, Topology Appl., 81 (1997), 185-196. Zbl0885.54019MR1485766DOI10.1016/S0166-8641(97)00031-X
  6. LIN, S., Point-Countable Covers and Sequence-Covering Mappings, Beijing: Chinese Science Press, 2002 (in Chinese). Zbl1004.54001MR1939779
  7. LIN, S., A note on sequence-covering mappings, Acta Math. Hungar., 107 (2005), 187- 191. Zbl1081.54025MR2148582DOI10.1007/s10474-005-0189-8
  8. LIN, S. - YAN, P., Sequence-covering maps of metric spaces, Topology Appl., 109 (2001), 301-314. Zbl0966.54012MR1807392DOI10.1016/S0166-8641(99)00163-7
  9. LIN, S. - YAN, P., Notes on cfp-covers, Comment Math. Univ. Carolinae, 44 (2003), 295- 306. Zbl1100.54021MR2026164
  10. MICHAEL, E., ℵ 0 -spaces, J. Math. Mech., 15 (1966), 983-1002. MR206907
  11. PONOMAREV, V. I., Axiom of countability and continuous mappings, Bull. Pol. Acad. Math., 8 (1960), 127-133. Zbl0095.16301MR116314
  12. SIWIEC, F., Sequence-covering and countably bi-quotient mappings, General Topology Appl., 1 (1971), 143-154. Zbl0218.54016MR288737
  13. TANAKA, Y. - GE, Y., Around quotient compact images of metric spaces, and symmetric spaces, Houston J. Math., 32 (2006), 99-117. Zbl1102.54034MR2202355
  14. YAN, P., On strong sequence-covering compact mapppings, Northeastem Math J., 14 (1998), 341-344. Zbl0927.54030MR1685267

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