Condensations of paratopological groups

Abstract

We prove that every Hausdorff Lindelöf paratopological group with countable pseudocharacter admits a condensation onto a separable metrizable space. This result resolves a problem of M. Tkachenko. Also, we show that every regular (Hausdorff) ω-narrow semitopological (paratopological) group with countable Hausdorff number and countable pseudocharacter condenses onto a second countable Urysohn space.We show that each regular precompact paratopological group of countable pseudocharacter admits a continuous isomorphism onto a metrizable separable topological group. Also, we construct a Hausdorff precompact paratopological group with countable pseudocharacter which cannot be condensed onto a Hausdorff first countable space.