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...
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th-cmuir.6653943832-470002018-04-25T07:23:23Z Topological gyrogroups: Generalization of topological groups Watchareepan Atiponrat Agricultural and Biological Sciences © 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. 2018-04-25T07:08:50Z 2018-04-25T07:08:50Z 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/6653943832/47000 |
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Agricultural and Biological Sciences Watchareepan Atiponrat Topological gyrogroups: Generalization of topological groups |
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© 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. |
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Journal |
| author |
Watchareepan Atiponrat |
| author_facet |
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 |
| title_full_unstemmed |
Topological gyrogroups: Generalization of topological groups |
| title_sort |
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/6653943832/47000 |
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