{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:09:58Z","timestamp":1760234998678,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T00:00:00Z","timestamp":1626652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in a number of ways, including as a colimit of homeomorphism groups with a given compact support or as a subgroup of the homeomorphism group of its Stone-\u010cech compactification. A space is said to have the Compactly Supported Homeomorphism Property (CSHP) if these two topologies coincide. The authors provide necessary and sufficient conditions for finite products of ordinals equipped with the order topology to have CSHP. In addition, necessary conditions are presented for finite products and coproducts of spaces to have CSHP.<\/jats:p>","DOI":"10.3390\/axioms10030155","type":"journal-article","created":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T10:07:37Z","timestamp":1626689257000},"page":"155","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Long Colimits of Topological Groups III: Homeomorphisms of Products and Coproducts"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7927-8931","authenticated-orcid":false,"given":"Rafael","family":"Dahmen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00e1bor","family":"Luk\u00e1cs","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"593","DOI":"10.2307\/2371787","article-title":"Topologies for Homeomorphism Groups","volume":"68","author":"Arens","year":"1946","journal-title":"Am. J. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1080\/00029890.2005.11920266","article-title":"On homeomorphism groups and the compact open topology","volume":"112","author":"Dijkstra","year":"2005","journal-title":"Am. Math. Mon."},{"key":"ref_3","unstructured":"Osipov, A.V. (2020). On homeomorphism groups and the set-open topology. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1016\/j.topol.2005.06.012","article-title":"Topologizing homeomorphism groups of rim-compact spaces","volume":"153","year":"2006","journal-title":"Topol. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"106938","DOI":"10.1016\/j.topol.2019.106938","article-title":"Long colimits of topological groups I: Continuous maps and homeomorphisms","volume":"270","author":"Dahmen","year":"2020","journal-title":"Topol. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"107266","DOI":"10.1016\/j.topol.2020.107266","article-title":"Long colimits of topological groups II: Free groups and vector spaces","volume":"279","author":"Dahmen","year":"2020","journal-title":"Topol. Appl."},{"key":"ref_7","unstructured":"Engelking, R. (1989). General Topology. Sigma Series in Pure Mathematics, Heldermann Verlag. [2nd ed.]. Translated from the Polish by the author."},{"key":"ref_8","first-page":"369","article-title":"Stone-\u010cech compactifications of products","volume":"90","author":"Glicksberg","year":"1959","journal-title":"Trans. Amer. Math. Soc."},{"key":"ref_9","unstructured":"Jech, T. (2003). Set Theory. The Third Millennium Edition, Revised and Expanded, Springer. [3rd ed.]."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gillman, L., and Jerison, M. (1960). Rings of Continuous Functions, D. Van Nostrand Co., Inc.. The University Series in Higher Mathematics.","DOI":"10.1007\/978-1-4615-7819-2"},{"key":"ref_11","unstructured":"Sierpi\u0144ski, W. (1965). Cardinal and Ordinal Numbers, PWN\u2014Panstwowe Wydawnictwo Naukowe. [2nd ed.]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/3\/155\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:31:45Z","timestamp":1760164305000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/3\/155"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,19]]},"references-count":11,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["axioms10030155"],"URL":"https:\/\/doi.org\/10.3390\/axioms10030155","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,7,19]]}}}