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THE k-QUOTIENT IMAGES OF METRIC SPACES

Shou Lin|Chunyan Zheng
대한수학회 (The Korean Mathematical Society)|2012.04|대한수학회논문집 (Communications of the KMS)|제27권 제2호|pp. 377-384

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참고문헌

키워드

connectednesssequentially closed sets$k$-closed sets$k$-quotient mappingssequentially quotient mappings
주제분류수학

초록

In this paper some properties of sequentially closed sets and $k$-closed sets in a topological space are discussed, it is shown that a space is a $k$-quotient image of a metric space if and only if its each sequentially closed set is $k$-closed, and some related examples about connectedness are obtained.

Abstract

In this paper some properties of sequentially closed sets and $k$-closed sets in a topological space are discussed, it is shown that a space is a $k$-quotient image of a metric space if and only if its each sequentially closed set is $k$-closed, and some related examples about connectedness are obtained.

참고문헌 (13)

  1. J. R. Boone, "On k-quotient mappings", Pacic J. Math, 51(2), pp.369~377 (1974)
  2. J. R. Boone, "Sequentially quotient mappings", Czechoslovak Math. J, 26(2), pp.174~182 (1976)
  3. C. R. Borges, "A note on dominated spaces", Acta Math. Hungar, 58(1-2), pp.13~16 (1991)
  4. A. Csaszar, "On k-connected sets", Acta Math. Hungar, 101(4), pp.273~279 (2003)
  5. R. Engelking, "General Topology" (1989), Heldermann Verlag
  6. A. Fedeli, "On good connected preimages", Topology Appl, 125(3), pp.489~496 (2002)
  7. S. P. Franklin, "Spaces in which sequences suffice", Fund. Math, 57(1), pp.107~115 (1965)
  8. Q. Huang, "Notes on sequentially connected spaces", Acta Math. Hungar, 110(1-2), pp.159~164 (2006)
  9. S. Lin, "Topologies of Metric Spaces and Function Spaces" (2004), Chinese Science Press
  10. S. Lin, "Some problems on generalized metrizable spaces, In E. Pearl ed., Open Prob- lems in Topology II", pp.731~736 (2007), Elsevier Science B. V
  11. P. J. Nyikos, "Classic problems, In Problems from Topology Proceedings", pp.69~89 (2003), Topology Atlas
  12. L. A. Steen, "Seebach, Counterexamples in Topology" (1978), Springer-Verlag
  13. C. Zheng, "On k-connected spaces", Far East J. Math. Sci, 25(1), pp.37~48 (2007)

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