Paratopological groups with countable strong Hausdorff number

摘要

This paper is dedicated to Professor Jinjin Li on the occasion of his 60th anniversary. In this paper, a new cardinal function called the strong Hausdorff number in semitopological groups is introduced. We mainly show that every paratopological group with countable strong Hausdorff number is omega-admissible. Applying this result, we prove that every bounded set in a paratopological group with countable strong Hausdorff number is strongly bounded, which partially answers to a question posed by Sanchez and Tkachenko. (C) 2020 Elsevier B.V. All rights reserved.