Commentationes mathematicae Universitatis Carolinae | |
Paratopological (topological) groups with certain networks | |
Chuan Liu1  | |
关键词: paratopological groups; topological groups; sequential neighborhood; networks; metrizable; compactifications; remainders; | |
DOI : | |
学科分类:物理化学和理论化学 | |
来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics | |
【 摘 要 】
In this paper, we discuss certain networks on paratopological (or topological) groups and give positive or negative answers to the questions in \cite{Lin2013}. We also prove that a non-locally compact, $k$-gentle paratopological group is metrizable if its remainder (in the Hausdorff compactification) is a Fr\'echet-Urysohn space with a point-countable cs*-network, which improves some theorems in [Liu C., {\it Metrizability of paratopological $($semitopological$)$ groups\/}, Topology Appl. {\bf 159} (2012), 1415--1420], [Liu C., Lin S., {\it Generalized metric spaces with algebraic structures\/}, Topology Appl. {\bf 157} (2010), 1966--1974].
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO201901237003487ZK.pdf | 47KB | download |