Feathered gyrogroups and gyrogroups with countable pseudocharacter

Abstract

Topological gyrogroups, with a weaker algebraic structure than groups, have been investigated recently. In this paper, ones prove that every feathered $N$-gyrogroup is paracompact, which implies that every feathered $N$-gyrogroup is a $D$-space and gives partial answers to two questions posed by A.V.Arhangel' ski\v\i ~(2010) in \cite{AA1}. Moreover, ones prove that every locally compact $NSS$-gyrogroup is first-countable. Finally, ones prove that each Lindel\"{o}f $P$-gyrogroup is Ra$\check{\imath}$kov complete.