Pseudocompact paratopological groups that are topological

2014/06/08 by Ravsky, Alex
#22A15 (Primary) 54H99 54H11 (Secondary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1406.2001

Abstract

We obtain necessary and sufficient conditions when a pseudocompact paratopological group is topological. (2-)pseudocompact and countably compact paratopological groups that are not topological are constructed. It is proved that each 2-pseudocompact paratopological group is pseudocompact and that each Hausdorff σ-compact pseudocompact paratopological group is a compact topological group. Our particular attention is devoted to periodic and topologically periodic pseudocompact paratopological groups.

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