Remainders of Semitopological Groups or Paratopological Groups

被引:1
|
作者
Lin, Fucai [1 ]
Liu, Chuan [2 ]
Xie, Li-Hong [3 ]
机构
[1] Minnan Normal Univ, Minnan, Peoples R China
[2] Ohio Univ, Athens, OH 45701 USA
[3] Wuji Univ, Fuzhou, Fujian, Peoples R China
关键词
TOPOLOGICAL-GROUPS; SPACES; COMPACTIFICATIONS; METRIZABILITY;
D O I
10.1007/s11253-014-0953-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 pi -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 a"e(1)-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'skNuC and M. M. Choban (Topology Proc., 37, 33-60 (2011)). Moreover, some open questions are formulated.
引用
收藏
页码:561 / 571
页数:11
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