arXiv 2103.115662021-03-22math.GN

The strong Pytkeev property and strong countable completeness in (strongly) topological gyrogroups

Meng Bao, Xiaoyuan Zhang, Xiaoquan Xu

备注：: 14 pages

英文摘要：

A topological gyrogroup is a gyrogroup endowed with a topology such that the binary operation is jointly continuous and the inverse mapping is also continuous. In this paper, it is proved that if $G$ is a sequential topological gyrogroup with an $ω^ω$-base, then $G$ has the strong Pytkeev property. Moreover, some equivalent conditions about $ω^ω$-base and strong Pytkeev property are given in Baire topological gyrogroups. Finally, it is shown that if $G$ is a strongly countably complete strongly topological gyrogroup, then $G$ contains a closed, countably compact, admissible subgyrogroup $P$ such that the quotient space $G/P$ is metrizable and the canonical homomorphism $π:G\rightarrow G/P$ is closed.

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