A supplement on feathered 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. It is shown that each compact subset of a topological gyrogroup with an ω ω -base is metrizable, which deduces that if G is a topological gyrogroup with an ω ωbase and is a k-space, then it is sequential. Moreover, for a feathered strongly topological gyrogroup G, based on the characterization of feathered strongly topological gyrogroups, we show that if G has countable cs * -character, then it is metrizable; and it is also shown that G has a compact resolution swallowing the compact sets if and only if G contains a compact L-subgyrogroup H such that the quotient space G/H is a Polish space.