Topological gyrogroups: Generalization of topological groups
© 2017 Elsevier B.V. Left Bol loops with the A ℓ -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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Journal |
| Published: |
2017
|
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85026319672&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40355 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| id |
th-cmuir.6653943832-40355 |
|---|---|
| record_format |
dspace |
| spelling |
th-cmuir.6653943832-403552017-09-28T04:09:02Z Topological gyrogroups: Generalization of topological groups Atiponrat W. © 2017 Elsevier B.V. Left Bol loops with the A ℓ -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 T 0 and T 3 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. 2017-09-28T04:09:02Z 2017-09-28T04:09:02Z Journal 01668641 2-s2.0-85026319672 10.1016/j.topol.2017.04.004 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85026319672&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40355 |
| institution |
Chiang Mai University |
| building |
Chiang Mai University Library |
| country |
Thailand |
| collection |
CMU Intellectual Repository |
| description |
© 2017 Elsevier B.V. Left Bol loops with the A ℓ -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 T 0 and T 3 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. |
| format |
Journal |
| author |
Atiponrat W. |
| spellingShingle |
Atiponrat W. Topological gyrogroups: Generalization of topological groups |
| author_facet |
Atiponrat W. |
| author_sort |
Atiponrat W. |
| title |
Topological gyrogroups: Generalization of topological groups |
| title_short |
Topological gyrogroups: Generalization of topological groups |
| title_full |
Topological gyrogroups: Generalization of topological groups |
| title_fullStr |
Topological gyrogroups: Generalization of topological groups |
| title_full_unstemmed |
Topological gyrogroups: Generalization of topological groups |
| title_sort |
topological gyrogroups: generalization of topological groups |
| publishDate |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85026319672&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40355 |
| _version_ |
1681421794430418944 |