Paratopological (topological) groups with certain networks

Commentationes mathematicae Universitatis Carolinae

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