A note on paratopological groups

Chuan Liu

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 4, page 633-640
  • ISSN: 0010-2628

Abstract

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In this paper, it is proved that a first-countable paratopological group has a regular G δ -diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [Spaces with a regular G δ -diagonal, Topology Appl. 153 (2006), 1917–1929]. If G is a symmetrizable paratopological group, then G is a developable space. We also discuss copies of S ω and of S 2 in paratopological groups and generalize some Nyikos [Metrizability and the Fréchet-Urysohn property in topological groups, Proc. Amer. Math. Soc. 83 (1981), no. 4, 793–801] and Svetlichnyi [Intersection of topologies and metrizability in topological groups, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 4 (1989), 79–81] results.

How to cite

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Liu, Chuan. "A note on paratopological groups." Commentationes Mathematicae Universitatis Carolinae 47.4 (2006): 633-640. <http://eudml.org/doc/249864>.

@article{Liu2006,
abstract = {In this paper, it is proved that a first-countable paratopological group has a regular $G_\{\delta \}$-diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [Spaces with a regular $G_\{\delta \}$-diagonal, Topology Appl. 153 (2006), 1917–1929]. If $G$ is a symmetrizable paratopological group, then $G$ is a developable space. We also discuss copies of $S_\omega $ and of $S_2$ in paratopological groups and generalize some Nyikos [Metrizability and the Fréchet-Urysohn property in topological groups, Proc. Amer. Math. Soc. 83 (1981), no. 4, 793–801] and Svetlichnyi [Intersection of topologies and metrizability in topological groups, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 4 (1989), 79–81] results.},
author = {Liu, Chuan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {paratopological group; symmetrizable spaces; regular $G_\{\delta \}$-diagonal; weak bases; Arens space; paratopological group; symmetrizable spaces; regular -diagonal; weak bases; Arens space},
language = {eng},
number = {4},
pages = {633-640},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on paratopological groups},
url = {http://eudml.org/doc/249864},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Liu, Chuan
TI - A note on paratopological groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 4
SP - 633
EP - 640
AB - In this paper, it is proved that a first-countable paratopological group has a regular $G_{\delta }$-diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [Spaces with a regular $G_{\delta }$-diagonal, Topology Appl. 153 (2006), 1917–1929]. If $G$ is a symmetrizable paratopological group, then $G$ is a developable space. We also discuss copies of $S_\omega $ and of $S_2$ in paratopological groups and generalize some Nyikos [Metrizability and the Fréchet-Urysohn property in topological groups, Proc. Amer. Math. Soc. 83 (1981), no. 4, 793–801] and Svetlichnyi [Intersection of topologies and metrizability in topological groups, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 4 (1989), 79–81] results.
LA - eng
KW - paratopological group; symmetrizable spaces; regular $G_{\delta }$-diagonal; weak bases; Arens space; paratopological group; symmetrizable spaces; regular -diagonal; weak bases; Arens space
UR - http://eudml.org/doc/249864
ER -

References

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