Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Compact-covering maps and $k$-networks
HTML articles powered by AMS MathViewer

by Huaipeng Chen PDF
Proc. Amer. Math. Soc. 131 (2003), 2623-2632 Request permission

Abstract:

In this paper, we show a characterization of compact-covering $s$-images of metric spaces and prove a theorem about them. Also we give a set theoretical assumption and under the assumption construct a counterexample which gives a negative answer to some questions.
References
  • Huaipeng Chen, Weak neighborhoods and Michael-Nagami’s question, Houston J. Math. 25 (1999), no. 2, 297–309. MR 1697627
  • L. Foged, Point-countable bases and $k$-networks, Topology Appl. 69 (1996), no. 2, 101–114. MR 1381683, DOI 10.1016/0166-8641(95)00100-X
  • G. Gruenhage, E. Michael, and Y. Tanaka, Spaces determined by point-countable covers, Pacific J. Math. 113 (1984), no. 2, 303–332. MR 749538
  • Takao Hoshina, On the quotient $s$-images of metric spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 10 (1970), 265–268 (1970). MR 275358
  • Shou Lin and Chuan Liu, On spaces with point-countable cs-networks, Proceedings of the International Conference on Set-theoretic Topology and its Applications (Matsuyama, 1994), 1996, pp. 51–60. MR 1425925, DOI 10.1016/S0166-8641(96)00043-0
  • C. Liu, and M. Dai, The compact-covering s-images of metric spaces, (Chinese) Acta Mathematica Sinica, 39(1996), 41-44.
  • S. Lin, On spaces with a $k$-network consisting of compact subsets, Top. Proc., Vol. 20,(1995), 185-190.
  • Zha Owen Li and Jin Jing Li, On Michael-Nagami’s problem, Questions Answers Gen. Topology 12 (1994), no. 1, 85–91. MR 1259473
  • E. Michael, Personal Letter.
  • E. Michael, Some problems, Open Problems in Topology, North-Holland, 1990, 273-278.
  • E. Michael and K. Nagami, Compact-covering images of metric spaces, Proc. Amer. Math. Soc. 37 (1973), 260–266. MR 307148, DOI 10.1090/S0002-9939-1973-0307148-4
  • Arnold W. Miller, Special subsets of the real line, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 201–233. MR 776624
  • Mary Ellen Rudin, Lectures on set theoretic topology, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 23, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, R.I., 1975. Expository lectures from the CBMS Regional Conference held at the University of Wyoming, Laramie, Wyo., August 12–16, 1974. MR 0367886
  • PROBLEM SECTION in topology proceedings, Volume 20, 1995.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54C10, 54G20, 04A15
  • Retrieve articles in all journals with MSC (1991): 54C10, 54G20, 04A15
Additional Information
  • Huaipeng Chen
  • Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
  • Email: hpchen@nankai.edu.cn
  • Received by editor(s): January 25, 2000
  • Received by editor(s) in revised form: March 25, 2002
  • Published electronically: November 13, 2002
  • Additional Notes: This work was supported by The Project-sponsored by SRF for ROCS, SEM
  • Communicated by: Alan Dow
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 2623-2632
  • MSC (1991): Primary 54C10, 54G20; Secondary 04A15
  • DOI: https://doi.org/10.1090/S0002-9939-02-06768-0
  • MathSciNet review: 1974664