@article{Lin_Liu_Xie_2014, title={Remainders of Semitopological Groups or Paratopological Groups}, volume={66}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2152}, abstractNote={We mainly discuss the remainders of Hausdorff compactifications of paratopological groups or semitopological groups. Thus, we show that if a nonlocally compact semitopological group <em class="a-plus-plus">G</em> has a compactification <em class="a-plus-plus">bG</em> such that the remainder <em class="a-plus-plus">Y</em> = <em class="a-plus-plus">bG \ G</em> possesses a locally countable network, then <em class="a-plus-plus">G</em> has a countable <em class="a-plus-plus">π</em> -character and is also first-countable, that if <em class="a-plus-plus">G</em> is a nonlocally compact semitopological group with locally metrizable remainder, then <em class="a-plus-plus">G</em> and <em class="a-plus-plus">bG</em> are separable and metrizable, that if a nonlocally compact paratopological group has a remainder with sharp base, then <em class="a-plus-plus">G</em> and <em class="a-plus-plus">bG</em> are separable and metrizable, and that if a nonlocally compact ℝ<sub class="a-plus-plus">1</sub>-factorizable paratopological group has a remainder which is a <em class="a-plus-plus">k</em> -semistratifiable space, then <em class="a-plus-plus">G</em> and <em class="a-plus-plus">bG</em> are separable and metrizable. These results improve some results obtained by C. Liu (Topology Appl., <strong class="a-plus-plus">159</strong>, 1415–1420 (2012)) and A.V. Arhangel’skїǐ and M. M. Choban (Topology Proc., <strong class="a-plus-plus">37</strong&gt;, 33–60 (2011)). Moreover, some open questions are formulated.}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Lin, Fucai and Liu, Chuan and Xie, Li-Hong}, year={2014}, month={Apr.}, pages={500–509} }