On weak-open π -images of metric spaces

Zhaowen Li

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 1011-1018
  • ISSN: 0011-4642

Abstract

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In this paper, we give some characterizations of metric spaces under weak-open π -mappings, which prove that a space is g -developable (or Cauchy) if and only if it is a weak-open π -image of a metric space.

How to cite

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Li, Zhaowen. "On weak-open $\pi $-images of metric spaces." Czechoslovak Mathematical Journal 56.3 (2006): 1011-1018. <http://eudml.org/doc/31087>.

@article{Li2006,
abstract = {In this paper, we give some characterizations of metric spaces under weak-open $\pi $-mappings, which prove that a space is $g$-developable (or Cauchy) if and only if it is a weak-open $\pi $-image of a metric space.},
author = {Li, Zhaowen},
journal = {Czechoslovak Mathematical Journal},
keywords = {weak-open mappings; $\pi $-mappings; $g$-developable spaces; Cauchy spaces; cs-covers; sn-covers; weak-developments; point-star networks; weak-open mappings; -mappings; -developable spaces; Cauchy spaces},
language = {eng},
number = {3},
pages = {1011-1018},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On weak-open $\pi $-images of metric spaces},
url = {http://eudml.org/doc/31087},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Li, Zhaowen
TI - On weak-open $\pi $-images of metric spaces
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 1011
EP - 1018
AB - In this paper, we give some characterizations of metric spaces under weak-open $\pi $-mappings, which prove that a space is $g$-developable (or Cauchy) if and only if it is a weak-open $\pi $-image of a metric space.
LA - eng
KW - weak-open mappings; $\pi $-mappings; $g$-developable spaces; Cauchy spaces; cs-covers; sn-covers; weak-developments; point-star networks; weak-open mappings; -mappings; -developable spaces; Cauchy spaces
UR - http://eudml.org/doc/31087
ER -

References

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  1. 10.1070/RM1966v021n04ABEH004169, Russian Math. Surveys 21 (1996), 115–162. (1996) MR0227950DOI10.1070/RM1966v021n04ABEH004169
  2. Axioms of countability of continuous mappings, Bull. Pol. Acad. Math. 8 (1960), 127–133. (1960) MR0116314
  3. On defining a space by a weak-base, Pacific J. Math. 52 (1974), 233–245. (1974) Zbl0285.54022MR0350706
  4. Characterizations of certain g -first countable spaces, Adv. Math. 29 (2000), 61–64. (2000) Zbl0999.54010MR1769127
  5. Symmetric spaces, g -developable space and g -metrizable spaces, Math. Japonica 36 (1991), 71–84. (1991) MR1093356
  6. The condition of metrizability of topological spaces and the axiom of symmetry, Mat. Sb. 3 (1938), 663–672. (1938) 
  7. 10.2140/pjm.1976.65.113, Pacific J.  Math. 65 (1976), 113–118. (1976) Zbl0359.54022MR0423307DOI10.2140/pjm.1976.65.113
  8. 10.4064/fm-57-1-107-115, Fund. Math. 57 (1965), 107–115. (1965) Zbl0132.17802MR0180954DOI10.4064/fm-57-1-107-115
  9. Generalized Metric Spaces and Mappings, Chinese Scientific Publ., Beijing, 1995. (1995) 
  10. On sequence-covering s -mappings, Adv. Math. 25 (1996), 548–551. (1996) Zbl0864.54026MR1453163
  11. On sequence-covering π -mappings, Acta Math. Sinica 45 (2002), 1157–1164. (2002) MR1959486
  12. 10.4064/fm-57-1-91-96, Fund. Math. 57 (1965), 91–96. (1965) Zbl0134.41802MR0179763DOI10.4064/fm-57-1-91-96
  13. On a new class of spaces and some problems of symmetrizability theory, Soviet Math. Dokl. 10 (1969), 845–848. (1969) Zbl0202.53702
  14. 10.1090/S0002-9939-1972-0290328-3, Proc. Amer. Math. Soc. 33 (1972), 161–164. (1972) Zbl0233.54015MR0290328DOI10.1090/S0002-9939-1972-0290328-3
  15. 10.1016/S0166-8641(01)00145-6, Topology Appl. 122 (2002), 237–252. (2002) MR1919303DOI10.1016/S0166-8641(01)00145-6
  16. Generalized metric spaces, In: Handbook of Set-theoretic Topology, K. Kunen, J. E. Vaughan (eds.), North-Holland, Amsterdam, 1984, pp. 423–501. (1984) Zbl0555.54015MR0776629
  17. Certain covering-maps and k -networks, and related matters, Topology Proc. 27 (2003), 317–334. (2003) Zbl1075.54010MR2048941
  18. 10.1023/B:CMAJ.0000042377.80659.fb, Czechoslovak Math.  J. 54 (2004), 393–400. (2004) Zbl1080.54509MR2059259DOI10.1023/B:CMAJ.0000042377.80659.fb

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