Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777966 | Topology and its Applications | 2017 | 10 Pages |
Abstract
Left Bol loops with the Aâ-property or gyrogroups are generalization of groups which do not explicitly have associativity. In this work, we define topological gyrogroups and study some properties of them. In spite of having a weaker algebraic form, topological gyrogroups carry almost the same basic properties owned by topological groups. In particular, we prove that being T0 and T3 are equivalent in topological gyrogroups. Furthermore, a topological gyrogroup is first countable if and only if it is premetrizable. Finally, a direct product of topological gyrogroups is a topological gyrogroup.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Watchareepan Atiponrat,