Conditions on Topological Gyrogroups to Embed in Topological Groups
A topological gyrogroup is a topological space endowed with a compatible nonassociative operation, which shares several common properties with topological groups. In this thesis, we prove that every locally compact Hausdorff topological gyrogroup G can be embedded in a completely regular topological...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Theses and Dissertations |
| Language: | English |
| Published: |
เชียงใหม่ : บัณฑิตวิทยาลัย มหาวิทยาลัยเชียงใหม่
2020
|
| Online Access: | http://cmuir.cmu.ac.th/jspui/handle/6653943832/69563 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | A topological gyrogroup is a topological space endowed with a compatible nonassociative operation, which shares several common properties with topological groups. In this thesis, we prove that every locally compact Hausdorff topological gyrogroup G can be embedded in a completely regular topological group I as a twisted subgroup. We also study properties shared by them by proving that G has property P if and only if T(G, Agyr) has property P, where P is one of the following properties: connectedness, path connectedness, and separability, and Agyr is the subgroup of the symmetric group on G generated by all the gyroautomorphisms of G. |
|---|