π -mappings in l s -Ponomarev-systems

Nguyen Van Dung

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 1, page 35-49
  • ISSN: 0044-8753

Abstract

top
We use the l s -Ponomarev-system ( f , M , X , { 𝒫 λ , n } ) , where M is a locally separable metric space, to give a consistent method to construct a π -mapping (compact mapping) with covering-properties from a locally separable metric space M onto a space X . As applications of these results, we systematically get characterizations of certain π -images (compact images) of locally separable metric spaces.

How to cite

top

Van Dung, Nguyen. "$\pi $-mappings in $ls$-Ponomarev-systems." Archivum Mathematicum 047.1 (2011): 35-49. <http://eudml.org/doc/116532>.

@article{VanDung2011,
abstract = {We use the $ls$-Ponomarev-system $(f, M, X, \lbrace \mathcal \{P\}_\{\lambda ,n\}\rbrace )$, where $M$ is a locally separable metric space, to give a consistent method to construct a $\pi $-mapping (compact mapping) with covering-properties from a locally separable metric space $M$ onto a space $X$. As applications of these results, we systematically get characterizations of certain $\pi $-images (compact images) of locally separable metric spaces.},
author = {Van Dung, Nguyen},
journal = {Archivum Mathematicum},
keywords = {sequence-covering; compact-covering; pseudo-sequence-covering; sequentially-quotient; $\pi $-mapping; $ls$-Ponomarev-system; double point-star cover; sequence-covering; compact-covering; pseudo-sequence-covering; sequentially-quotient; -mapping; -Ponomarev-system; double point-star cover},
language = {eng},
number = {1},
pages = {35-49},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$\pi $-mappings in $ls$-Ponomarev-systems},
url = {http://eudml.org/doc/116532},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Van Dung, Nguyen
TI - $\pi $-mappings in $ls$-Ponomarev-systems
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 1
SP - 35
EP - 49
AB - We use the $ls$-Ponomarev-system $(f, M, X, \lbrace \mathcal {P}_{\lambda ,n}\rbrace )$, where $M$ is a locally separable metric space, to give a consistent method to construct a $\pi $-mapping (compact mapping) with covering-properties from a locally separable metric space $M$ onto a space $X$. As applications of these results, we systematically get characterizations of certain $\pi $-images (compact images) of locally separable metric spaces.
LA - eng
KW - sequence-covering; compact-covering; pseudo-sequence-covering; sequentially-quotient; $\pi $-mapping; $ls$-Ponomarev-system; double point-star cover; sequence-covering; compact-covering; pseudo-sequence-covering; sequentially-quotient; -mapping; -Ponomarev-system; double point-star cover
UR - http://eudml.org/doc/116532
ER -

References

top
  1. An, T. V., Dung, N. V., 10.1155/2008/145683, Internat. J. Math. Math. Sci. (2008), 1–8. (2008) Zbl1147.54318DOI10.1155/2008/145683
  2. An, T. V., Dung, N. V., 10.1134/S1995080208030013, Lobachevskii J. Math. 29 (2008 (3)), 111–118. (2008) Zbl1168.54013MR2434889DOI10.1134/S1995080208030013
  3. Arhangel’skii, A. V., 10.1070/RM1966v021n04ABEH004169, Russian Math. Surveys 21 (1966), 115–162. (1966) MR0227950DOI10.1070/RM1966v021n04ABEH004169
  4. Boone, J. R., Siwiec, F., Sequentially quotient mappings, Czechoslovak Math. J. 26 (1976), 174–182. (1976) Zbl0334.54003MR0402689
  5. Engelking, R., General topology, PWN – Polish Scientific Publishers, Warsaw, 1977. (1977) Zbl0373.54002MR0500780
  6. Ge, Y., On compact images of locally separable metric spaces, Topology Proc. 27 (1) (2003), 351–360. (2003) Zbl1072.54020MR2048944
  7. Ge, Y., On pseudo–sequence–covering π –images of metric spaces, Mat. Vesnik 57 (2005), 113–120. (2005) MR2194600
  8. Ge, Y., On three equivalences concerning Ponomarev–systems, Arch. Math. (Brno) 42 (2006), 239–246. (2006) Zbl1164.54363MR2260382
  9. Ikeda, Y., Liu, C., Tanaka, Y., 10.1016/S0166-8641(01)00145-6, Topology Appl. 122 (2002), 237–252. (2002) Zbl0994.54015MR1919303DOI10.1016/S0166-8641(01)00145-6
  10. Li, Z., 10.1155/IJMMS.2005.1101, nternat. J. Math. Math. Sci. 7 (2005), 1101–1107. (2005) Zbl1082.54023DOI10.1155/IJMMS.2005.1101
  11. Lin, S., Point-countable covers and sequence-covering mappings, Chinese Science Press, Beijing, 2002. (2002) Zbl1004.54001MR1939779
  12. Lin, S., Liu, C, Dai, M., 10.1007/BF02560519, Acta Math. Sinica (N.S.) 13 (1) (1997), 1–8. (1997) Zbl0881.54014MR1465530DOI10.1007/BF02560519
  13. Lin, S., Yan, P., Notes on c f p -covers, Comment. Math. Univ. Carolin. 44 (2) (2003), 295–306. (2003) Zbl1100.54021MR2026164
  14. Michael, E., 10.1007/BF02759940, Israel J. Math. 2 (1964), 173–176. (1964) MR0177396DOI10.1007/BF02759940
  15. Michael, E., ℵ 0 –spaces, J. Math. Mech. 15 (1966), 983–1002. (1966) MR0206907
  16. Ponomarev, V. I., Axiom of countability and continuous mappings, Bull. Polish Acad. Sci. Math. 8 (1960), 127–133. (1960) MR0116314
  17. Siwiec, F., 10.1016/0016-660X(71)90120-6, General Topology Appl. 1 (1971), 143–154. (1971) Zbl0218.54016MR0288737DOI10.1016/0016-660X(71)90120-6
  18. Tanaka, Y., Theory of k –networks II, Questions Answers Gen. Topology 19 (2001), 27–46. (2001) Zbl0970.54023MR1815344
  19. Tanaka, Y., Ge, Y., Around quotient compact images of metric spaces, and symmetric spaces, Houston J. Math. 32 (1) (2006), 99–117. (2006) Zbl1102.54034MR2202355
  20. Yan, P., On the compact images of metric spaces, J. Math. Study 30 (2) (1997), 185–187. (1997) MR1468151
  21. Yan, P., On strong sequence–covering compact mappings, Northeast. Math. J. 14 (1998), 341–344. (1998) Zbl0927.54030MR1685267

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.