k-semistratifiable spaces and expansions of set-valued mappings


  • Peng-Fei Yan Wuyi University
  • Xing-Yu Hu Wuyi University
  • Li-Hong Xie Wuyi University




locally bounded set-valued mappings, k-MCM spaces, k-semistratifiable spaces, lower semi-continuous (l.s.c.), k-upper semi-continuous (k-u.s.c.)


In this paper, the concept of k-upper semi-continuous set-valued mappings is introduced. Using this concept, we give characterizations of k-semistratifiable and k-MCM spaces, which answers a question posed by Xie and Yan.


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Author Biographies

Peng-Fei Yan, Wuyi University

School of Mathematics and Computational Science

Xing-Yu Hu, Wuyi University

School of Mathematics and Computational Science

Li-Hong Xie, Wuyi University

School of Mathematics and Computational Science


G. D. Creede, Semi-stratifiable, in: Proc Arizona State Univ Topological Conf. (1967, 1969), 318-323.

R. Engelking, General topology, Revised and completed edition, Heldermann Verlag, 1989.

C. Good, R. Knight and I. Stares, Monotone countable paracompactness, Topology Appl. 101 (2000), 281-298. https://doi.org/10.1016/S0166-8641(98)00128-X

D. L. Lutzer, Semistratifiable and stratifiable, General Topology Appl. 1 (1971), 43-48. https://doi.org/10.1016/0016-660X(71)90109-7

J. Mack, On a class of countably paracompact spaces, Proc. Amer. Math. Soc. 16 (1965), 467-472. https://doi.org/10.1090/S0002-9939-1965-0177388-1

C. Pan, Monotonically CP spaces, Questions Ans. Gen. Topol. 15 (1997) 25-32.

L. X. Peng and S. Lin, On monotone spaces and metrization theorems, Acta. Math. Sinica 46 (2003), 1225-1232 (in Chinese).

L.-H. Xie, The insertions of semicontinuous functions and strafiable spaces, Master's thesis, Jiangmen: Wuyi University, 2010.

L.-H. Xie and P.-F. Yan, Expansions of set-valued mappings on stratifiable spaces, Houston J. Math. 43 (2017), 611-624.

K. Yamazaki, Locally bounded set-valued mappings and monotone countable paracompactness, Topology Appl. 154 (2007), 2817-2825. https://doi.org/10.1016/j.topol.2007.05.015




How to Cite

P.-F. Yan, X.-Y. Hu, and L.-H. Xie, “k-semistratifiable spaces and expansions of set-valued mappings”, Appl. Gen. Topol., vol. 19, no. 1, pp. 145–153, Apr. 2018.



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