Paratopological groups: local versus global (Q2219252)

An example is given in order to show that locally metrizable paratopological groups might be neither paracompact nor normal. This provides negative answers to questions previously posed in the field by \textit{A. Arhangel'skii} and \textit{M. Tkachenko} [Topological groups and related structures. Hackensack, NJ: World Scientific; Paris: Atlantis Press (2008; Zbl 1323.22001)] for paratopological groups. The authors also consider the conditions under which 2-pseudocompactness is a three space property in paratopological groups.