Embedding of locally compact Hausdorff topological gyrogroups in topological groups
© 2020 Elsevier B.V. A topological gyrogroup is a topological space endowed with a compatible nonassociative operation, which shares several common properties with topological groups. In this article, we prove that every locally compact Hausdorff topological gyrogroup G can be embedded in a complete...
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| Main Authors: | , , |
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| Format: | Journal |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079158985&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68454 |
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| Institution: | Chiang Mai University |
| Summary: | © 2020 Elsevier B.V. A topological gyrogroup is a topological space endowed with a compatible nonassociative operation, which shares several common properties with topological groups. In this article, we prove that every locally compact Hausdorff topological gyrogroup G can be embedded in a completely regular topological group Γ as a twisted subset. We also study properties shared by them by proving that G has property [Formula presented] if and only if Γ has property [Formula presented], where [Formula presented] is one of the following properties: connectedness, path connectedness, and separability. |
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