On locally p-spaces and remainders of semitopological groups
On locally p-spaces and remainders of semitopological groups
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关于局部 p 空间和半拓扑群的余数
DOI：
10.1016/j.topol.2019.03.019
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发表时间：
2019
影响因子：
0.6
通讯作者：
Jing Zhang
中科院分区：
文献类型：
--
作者：
Hanfeng Wang;Wei He;Jing Zhang
本文研究了局部p-空间是仿拓扑群的紧化问题，证明了：（1）若仿拓扑群X有局部p-空间的余项，则X是仿紧p-拓扑群，或X是稀疏的;（2）若非局部紧仿拓扑群X有局部p-空间的余项，则X是Lindelöf p-空间，或X是σ-紧的;（3）如果紧空间Z是两个非局部紧拓扑群X和Y的并，使得Z <$X是局部可展的，则Z是可分的和可度量化的;（4）若非局部紧Baire拓扑群G的余项Y是有限族可度量化子空间的并，则G是可度量化的.改进了AV Arhangel'skii等人的一些结果。
We study the compactification of semitopological groups with remainders being locally p⁎⁎-spaces, and establish:(1) if a semitopological group X has a remainder that is locally a p⁎⁎-space, then either X is a paracompact p-topological group, or X is meager;(2) if a non-locally compact paratopological group X has a remainder that is locally a p-space, then either X is a Lindelöf p-space, or X is σ-compact;(3) if a compact space Z is the union of two non-locally compact semitopological groups X and Y such that Z∖ X is locally developable, then Z is separable and metrizable;(4) if a non-locally compact Baire semitopological group G has a remainder Y that is the union of a finite family of metrizable subspaces, then G is metrizable. Some results of AV Arhangel'skii et al. are improved.