Abstract
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 ω-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 Sánchez and Tkachenko.
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