Quotient with respect to admissible L-subgyrogroups

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