Paratopological Groups: Local Versus Global

In this paper, one example is constructed to show that locally metrizable paratopological groups might be neither paracompact nor normal. It gives negative answers to two questions posed in A. Arhangel'skii and M. Tkachenko (2008) [1] in the case of paratopological groups. We also consider the conditions under which 2-pseudocompactness is a three space property in paratopological groups. (C) 2020 Elsevier B.V. All rights reserved.