{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T11:16:12Z","timestamp":1760181372621,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T00:00:00Z","timestamp":1604275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Center in Mathematics and Applied Mathematics, Chiang Mai University","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A gyrogroup, an algebraic structure that generalizes groups, is modeled on the bounded symmetric space of relativistically admissible velocities endowed with Einstein\u2019s addition. Given a gyrogroup G, we offer a new way to construct a gyrogroup G\u2022 such that G\u2022 contains a gyro-isomorphic copy of G. We then prove that every strongly topological gyrogroup G can be embedded as a closed subgyrogroup of the path-connected and locally path-connected topological gyrogroup G\u2022. We also study several properties shared by G and G\u2022, including gyrocommutativity, first countability and metrizability. As an application of these results, we prove that being a quasitopological gyrogroup is equivalent to being a strongly topological gyrogroup in the class of normed gyrogroups.<\/jats:p>","DOI":"10.3390\/sym12111817","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T09:04:46Z","timestamp":1604307886000},"page":"1817","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Embedding of Strongly Topological Gyrogroups in Path-Connected and Locally Path-Connected Gyrogroups"],"prefix":"10.3390","volume":"12","author":[{"given":"Jaturon","family":"Wattanapan","sequence":"first","affiliation":[{"name":"Doctoral Program in Mathematics, Graduate School, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5962-4032","authenticated-orcid":false,"given":"Watchareepan","family":"Atiponrat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1239-5586","authenticated-orcid":false,"given":"Teerapong","family":"Suksumran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,2]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Ungar, A.A. (2008). Analytic Hyperbolic Geometry and Albert Einstein\u2019s Special Theory of Relativity, World Scientific.","key":"ref_1","DOI":"10.1142\/9789812772305"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.topol.2017.04.004","article-title":"Topological gyrogroups: Generalization of topological groups","volume":"224","author":"Atiponrat","year":"2017","journal-title":"Topol. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5113","DOI":"10.2298\/FIL1916113B","article-title":"Feathered gyrogroups and gyrogroups with countable pseudocharacter","volume":"33","author":"Bao","year":"2019","journal-title":"Filomat"},{"doi-asserted-by":"crossref","unstructured":"Rassias, T.M., and Pardalos, P.M. (2019). On metric structures of normed gyrogroups. 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