Topological gyrogroups: Generalization of topological groups
© 2017 Elsevier B.V. Left Bol loops with the Aℓ-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 a...
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| Format: | Journal |
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2018
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| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85026319672&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57514 |
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| Institution: | Chiang Mai University |
| Summary: | © 2017 Elsevier B.V. Left Bol loops with the Aℓ-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 T0and T3are 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. |
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