Quotient with respect to admissible \(L\)-subgyrogroups. (English) Zbl 1473.54038
Summary: 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 the 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 generalizes that 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 \(\pi\) from \(G\) onto the quotient space \(G / H\) has some nice local properties, such as, local compactness, local pseudocompactness, and local paracompactness, etc. Finally, we prove that each locally paracompact strongly topological gyrogroup is paracompact.
MSC:
| 54H11 | Topological groups (topological aspects) |
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
| 20N05 | Loops, quasigroups |
| 18A32 | Factorization systems, substructures, quotient structures, congruences, amalgams |
| 20A05 | Axiomatics and elementary properties of groups |
| 20B30 | Symmetric groups |
Keywords:
topological gyrogroup; strongly topological gyrogroup; perfect mapping; locally compact; admissible subgyrogroup; \(L\)-subgyrogroup; paracompact spaceReferences:
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