Quotient with respect to admissible L-subgyrogroups
Abstract
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. A topological gyrogroup is just a gyrogroup endowed with a compatible topology such that the multiplication is jointly continuous and the inverse is continuous. This concept is a good generalization of a topological group. 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 π from G onto the quotient space G/H has some nice local properties, such as, local compactness, local pseudocompactness, local paracompactness, etc. Finally, we prove that each locally paracompact strongly topological gyrogroup is paracompact.