On reflections and three space properties of semi(para)topological groups

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• 作者：Liang-Xue Peng ; ^{pengliangxue@bjut.edu.cn} ; Ming-Yue Guo ^{guomingyue@emails.bjut.edu.cn}
• 关键词：primary ; 54H99 ; 54D10 ; secondary ; 54B30 ; 54C10
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：217
• 期：Complete
• 页码：107-115
• 全文大小：328 K
• 卷排序：217

文摘

We show that many topological properties are invariant and/or inverse invariant under taking T2T2-reflections in semitopological groups. We also extend some three space properties in topological groups (paratopological groups) to semitopological groups. The following result is established: Let G be a regular semitopological group and let H be a closed subgroup of G such that all compact (resp., countably compact, sequentially compact) subsets of the semitopological group H   are first-countable. If the quotient space G/HG/H has the following property, then so does the semitopological group G.(*) all compact (resp., countably compact, sequentially compact) subsets are Hausdorff and strongly Fréchet (strictly Fréchet).