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

Abstract

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 ωω -base, then G has the strong Pytkeev property. Moreover, some equivalent conditions about ωω -base and strongly 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 → G/P is closed.