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A note on paratopological groups. (English) Zbl 1150.54036
Summary: In this paper, it is proved that a first-countable paratopological group has a regular $$G_{\delta }$$-diagonal. 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.

##### MSC:
 54H13 Topological fields, rings, etc. (topological aspects) 54H99 Connections of general topology with other structures, applications
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