Paratopological (topological) groups with certain networks

Chuan Liu

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 1, page 111-119
  • ISSN: 0010-2628

Abstract

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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].

How to cite

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Liu, Chuan. "Paratopological (topological) groups with certain networks." Commentationes Mathematicae Universitatis Carolinae 55.1 (2014): 111-119. <http://eudml.org/doc/260774>.

@article{Liu2014,
abstract = {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].},
author = {Liu, Chuan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {paratopological groups; topological groups; sequential neighborhood; networks; metrizable; compactifications; remainders; paratopological group; topological group; sequential neighborhood; network; metrizable; compactification; remainder},
language = {eng},
number = {1},
pages = {111-119},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Paratopological (topological) groups with certain networks},
url = {http://eudml.org/doc/260774},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Liu, Chuan
TI - Paratopological (topological) groups with certain networks
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 1
SP - 111
EP - 119
AB - 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].
LA - eng
KW - paratopological groups; topological groups; sequential neighborhood; networks; metrizable; compactifications; remainders; paratopological group; topological group; sequential neighborhood; network; metrizable; compactification; remainder
UR - http://eudml.org/doc/260774
ER -

References

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