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:	Jaturon Wattanapan, Watchareepan Atiponrat, Teerapong Suksumran
Format:	Journal
Published:	2020
Subjects:	Mathematics
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

id	th-cmuir.6653943832-68454
record_format	dspace
spelling	th-cmuir.6653943832-684542020-04-02T15:27:38Z Embedding of locally compact Hausdorff topological gyrogroups in topological groups Jaturon Wattanapan Watchareepan Atiponrat Teerapong Suksumran Mathematics © 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. 2020-04-02T15:27:38Z 2020-04-02T15:27:38Z 2020-03-15 Journal 01668641 2-s2.0-85079158985 10.1016/j.topol.2020.107102 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079158985&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68454
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics Jaturon Wattanapan Watchareepan Atiponrat Teerapong Suksumran Embedding of locally compact Hausdorff topological gyrogroups in topological groups
description	© 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.
format	Journal
author	Jaturon Wattanapan Watchareepan Atiponrat Teerapong Suksumran
author_facet	Jaturon Wattanapan Watchareepan Atiponrat Teerapong Suksumran
author_sort	Jaturon Wattanapan
title	Embedding of locally compact Hausdorff topological gyrogroups in topological groups
title_short	Embedding of locally compact Hausdorff topological gyrogroups in topological groups
title_full	Embedding of locally compact Hausdorff topological gyrogroups in topological groups
title_fullStr	Embedding of locally compact Hausdorff topological gyrogroups in topological groups
title_full_unstemmed	Embedding of locally compact Hausdorff topological gyrogroups in topological groups
title_sort	embedding of locally compact hausdorff topological gyrogroups in topological groups
publishDate	2020
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079158985&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68454
_version_	1681426822916472832

Embedding of locally compact Hausdorff topological gyrogroups in topological groups

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