Geodesic
Paratopological (topological) groups with certain networks
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 1, pp. 111-119
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In this paper, we discuss certain networks on paratopological (or topological) groups and give positive or negative answers to the questions in [Lin2013]. We also prove that a non-locally compact, $k$-gentle paratopological group is metrizable if its remainder (in the Hausdorff compactification) is a Fréchet-Urysohn space with a point-countable cs*-network, which improves some theorems in [Liu C., Metrizability of paratopological $($semitopological$)$ groups, Topology Appl. 159 (2012), 1415--1420], [Liu C., Lin S., Generalized metric spaces with algebraic structures, Topology Appl. 157 (2010), 1966--1974].
In this paper, we discuss certain networks on paratopological (or topological) groups and give positive or negative answers to the questions in [Lin2013]. We also prove that a non-locally compact, $k$-gentle paratopological group is metrizable if its remainder (in the Hausdorff compactification) is a Fréchet-Urysohn space with a point-countable cs*-network, which improves some theorems in [Liu C., Metrizability of paratopological $($semitopological$)$ groups, Topology Appl. 159 (2012), 1415--1420], [Liu C., Lin S., Generalized metric spaces with algebraic structures, Topology Appl. 157 (2010), 1966--1974].
Classification : 54E20, 54E35, 54H11
Keywords: paratopological groups; topological groups; sequential neighborhood; networks; metrizable; compactifications; remainders 
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Liu, Chuan. Paratopological (topological) groups with certain networks. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 1, pp. 111-119. http://geodesic.mathdoc.fr/item/CMUC_2014_55_1_a8/