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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Main Author: Watchareepan Atiponrat
Format: Journal
Published: 2018
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/57514
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Institution: Chiang Mai University
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spelling 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
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Watchareepan Atiponrat
Topological gyrogroups: Generalization of topological groups
description © 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.
format Journal
author Watchareepan Atiponrat
author_facet Watchareepan Atiponrat
author_sort 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
publishDate 2018
url 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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