Long Colimits of Topological Groups III: Homeomorphisms of Products and Coproducts
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-Čech compactification. A space is said to have the <i&g...
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| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/155 |
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| author | Rafael Dahmen Gábor Lukács |
| author_facet | Rafael Dahmen Gábor Lukács |
| author_sort | Rafael Dahmen |
| collection | DOAJ |
| description | 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-Čech compactification. A space is said to have the <i>Compactly Supported Homeomorphism Property</i> (<i>CSHP</i>) 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. |
| first_indexed | 2024-03-10T07:54:02Z |
| format | Article |
| id | doaj.art-4258c56b1ae841109a56ee12490c1661 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T07:54:02Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-4258c56b1ae841109a56ee12490c16612023-11-22T12:02:12ZengMDPI AGAxioms2075-16802021-07-0110315510.3390/axioms10030155Long Colimits of Topological Groups III: Homeomorphisms of Products and CoproductsRafael Dahmen0Gábor Lukács1Department of Mathematics, Karlsruhe Institute of Technology, D-76128 Karlsruhe, GermanyDepartment of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5, CanadaThe 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-Čech compactification. A space is said to have the <i>Compactly Supported Homeomorphism Property</i> (<i>CSHP</i>) 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.https://www.mdpi.com/2075-1680/10/3/155long colimittopological grouphomeomorphism group |
| spellingShingle | Rafael Dahmen Gábor Lukács Long Colimits of Topological Groups III: Homeomorphisms of Products and Coproducts Axioms long colimit topological group homeomorphism group |
| title | Long Colimits of Topological Groups III: Homeomorphisms of Products and Coproducts |
| title_full | Long Colimits of Topological Groups III: Homeomorphisms of Products and Coproducts |
| title_fullStr | Long Colimits of Topological Groups III: Homeomorphisms of Products and Coproducts |
| title_full_unstemmed | Long Colimits of Topological Groups III: Homeomorphisms of Products and Coproducts |
| title_short | Long Colimits of Topological Groups III: Homeomorphisms of Products and Coproducts |
| title_sort | long colimits of topological groups iii homeomorphisms of products and coproducts |
| topic | long colimit topological group homeomorphism group |
| url | https://www.mdpi.com/2075-1680/10/3/155 |
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