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Ukrainian Mathematical Journal

, Volume 66, Issue 4, pp 561–571 | Cite as

Remainders of Semitopological Groups or Paratopological Groups

  • Fucai Lin
  • Chuan Liu
  • Li-Hong Xie
Article

We mainly discuss the remainders of Hausdorff compactifications of paratopological groups or semitopological groups. Thus, we show that if a nonlocally compact semitopological group G has a compactification bG such that the remainder Y = bG \ G possesses a locally countable network, then G has a countable π -character and is also first-countable, that if G is a nonlocally compact semitopological group with locally metrizable remainder, then G and bG are separable and metrizable, that if a nonlocally compact paratopological group has a remainder with sharp base, then G and bG are separable and metrizable, and that if a nonlocally compact ℝ1-factorizable paratopological group has a remainder which is a k -semistratifiable space, then G and bG are separable and metrizable. These results improve some results obtained by C. Liu (Topology Appl., 159, 1415–1420 (2012)) and A.V. Arhangel’skїǐ and M. M. Choban (Topology Proc., 37, 33–60 (2011)). Moreover, some open questions are formulated.

Keywords

Topological Group Metrizable Space Dense Subspace Countable Base Countable Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Fucai Lin
    • 1
  • Chuan Liu
    • 2
  • Li-Hong Xie
    • 3
  1. 1.Minnan Normal UniversityMinnanChina
  2. 2.Ohio UniversityZanesvilleUSA
  3. 3.Wuji UniversityNanpingChina

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