Chuan Liu
A note on paratopological groups

Comment.Math.Univ.Carolin. 47,4 (2006) 633-640.

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 Fr\'echet-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.

Keywords: paratopological group, symmetrizable spaces, regular $G_{\delta }$-diagonal, weak bases, Arens space
AMS Subject Classification: Primary 54H13, 54H99