Remainders of Semitopological Groups or Paratopological Groups
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.
English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 4, pp 561-571.
Citation Example: Lin Fucai, Liu Chuan, Xie Li-Hong Remainders of Semitopological Groups or Paratopological Groups // Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 500–509.