Chinese Quarterly Journal of Mathematics ›› 2016, Vol. 31 ›› Issue (1): 82-86.

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Two Notes on Topological Groups

  

  1. School of Mathematics and Statistics, Minnan Normal University
  • Received:2014-10-09 Online:2016-03-30 Published:2020-11-18
  • About author:ZHANG Ke-xiu(1978-), female, native of Linyi, Shandong, a lecturer of Minnan Normal University, engages in general topology; LIU Xin(1986-), male, native of Xinyang, Henan, a postgraduate of Minnan Normal University, engages in general topology; TANG Zhong-bao(1984-), male, native of Hengyang, Hunan, a postgraduate of Minnan Normal University, engages in general topology.
  • Supported by:
    Supported by the National Natural Science Foundation of China(11201414,11471153);

Abstract: In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense Gδ-set in a locally feebly compact regular space X. 

Key words: topological group, first-countable, paratopological group, locally feebly compact, metrizable

CLC Number: