Quotient with respect to admissible $L$-subgyrogroups

Meng Bao, Fucai Lin

Published 2020-03-18Version 1

The concept of gyrogroups, with a weaker algebraic structure without associative law, was introduced under the background of $c$-ball of relativistically admissible velocities with Einstein velocity addition. The class of topological gyrogroups is just the gyrogroups endowed with a compatible topology such that the multiplication is jointly continuous and the inverse is continuous, which is a good generalization of topological groups. In this paper, we are going to establish that for a locally compact admissible $L$-subgyrogroup $H$ of a strongly topological gyrogroup $G$, the natural quotient mapping $\pi$ of $G$ onto the quotient space $G/H$ has some rather nice properties locally, such as, locally compactness, local pseudocompactness, local paracompactness, etc.