The diagonal of a first countable paratopological group, submetrizability, and related results
Keywords:Gδ-diagonal of rank n, Semitopological and paratopological groups, Souslin number, Submetrizability
We discuss some properties stronger than Gδ-diagonal. Among other things, we prove that any first countable paratopological group has a Gδ-diagonal of infinite rank and hence also a regular Gδ-diagonal. This answer a question recently asked by Arhangel’skii and Burke.
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