Browse > Article
http://dx.doi.org/10.4134/CKMS.2012.27.2.377

THE κ-QUOTIENT IMAGES OF METRIC SPACES  

Lin, Shou (Department of Mathematics Zhangzhou Normal University, Institute of Mathematics Ningde Teachers' College)
Zheng, Chunyan (Institute of Mathematics Ningde Teachers' College)
Publication Information
Communications of the Korean Mathematical Society / v.27, no.2, 2012 , pp. 377-384 More about this Journal
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.
Keywords
sequentially closed sets; $k$-closed sets; $k$-quotient mappings; sequentially quotient mappings; connectedness;
Citations & Related Records
연도 인용수 순위
  • Reference
1 C. Zheng, On k-connected spaces, Far East J. Math. Sci. 25 (2007), no. 1, 37-48.
2 J. R. Boone, On k-quotient mappings, Pacific J. Math. 51 (1974), no. 2, 369-377.   DOI
3 J. R. Boone and F. Siwiec, Sequentially quotient mappings, Czechoslovak Math. J. 26(101) (1976), no. 2, 174-182.
4 C. R. Borges, A note on dominated spaces, Acta Math. Hungar. 58 (1991), no. 1-2, 13-16.   DOI
5 A. Csaszar, $\gamma$-connected sets, Acta Math. Hungar. 101 (2003), no. 4, 273-279.   DOI
6 R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
7 A. Fedeli and A. Le Donne, On good connected preimages, Topology Appl. 125 (2002), no. 3, 489-496.   DOI   ScienceOn
8 S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), no. 1, 107-115.
9 Q. Huang and S. Lin, Notes on sequentially connected spaces, Acta Math. Hungar. 110 (2006), no. 1-2, 159-164.   DOI
10 S. Lin, Topologies of Metric Spaces and Function Spaces, Chinese Science Press, Beijing, 2004.
11 S. Lin, Some problems on generalized metrizable spaces, In: E. Pearl ed., Open Problems in Topology II, Elsevier Science B. V., Amsterdam, 2007, 731-736.
12 P. J. Nyikos, Classic problems, In: E. Pearl ed., Problems from Topology Proceedings, Topology Atlas, Toronta, 2003, 69-89.
13 L. A. Steen and Jr J. A. Seebach, Counterexamples in Topology, Second Edition, Springer-Verlag, New York, 1978.