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<p>Bouziad proved that every semitopological group, which is a Baire <i>p</i>-space, is paratopological. We will prove that every semitopological group, which is a regular Baire locally <i>p</i>-space, is a completely regular paratopological group. We weaken both conditions of complete regularity and <i>p</i>-space. As a result we obtain that every semitopological group, which is a regular locally Čech-complete space, is a topological group.</p>

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A regular locally Čech-complete semitopological group is topological

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Ľubica Holá

摘要

Bouziad proved that every semitopological group, which is a Baire p-space, is paratopological. We will prove that every semitopological group, which is a regular Baire locally p-space, is a completely regular paratopological group. We weaken both conditions of complete regularity and p-space. As a result we obtain that every semitopological group, which is a regular locally Čech-complete space, is a topological group.