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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th-cmuir.6653943832-575142018-09-05T03:44:45Z Topological gyrogroups: Generalization of topological groups Watchareepan Atiponrat Mathematics © 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. 2018-09-05T03:44:45Z 2018-09-05T03:44:45Z 2017-06-15 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/6653943832/57514 |
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Mathematics Watchareepan Atiponrat Topological gyrogroups: Generalization of topological groups |
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© 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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Watchareepan Atiponrat |
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Watchareepan Atiponrat |
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Watchareepan Atiponrat |
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 |
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Topological gyrogroups: Generalization of topological groups |
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topological gyrogroups: generalization of topological groups |
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2018 |
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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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