Cofinite graphs and their profinite completions
<p>We generalize the idea of cofinite groups, due to B. Hartley, [2]. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions.</p><p>The idea of constructing a cofinite graph starts with defining a uniform top...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2017-10-01
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| Series: | Electronic Journal of Graph Theory and Applications |
| Subjects: | |
| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/222 |
| _version_ | 1818531909753372672 |
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| author | Amrita Acharyya Jon M Corson Bikash Das |
| author_facet | Amrita Acharyya Jon M Corson Bikash Das |
| author_sort | Amrita Acharyya |
| collection | DOAJ |
| description | <p>We generalize the idea of cofinite groups, due to B. Hartley, [2]. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions.</p><p>The idea of constructing a cofinite graph starts with defining a uniform topological graph $\Gamma$, in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over $\Gamma$. It is established that for any cofinite graph there exists a unique cofinite completion.</p> |
| first_indexed | 2024-12-11T17:38:37Z |
| format | Article |
| id | doaj.art-a290acb3f6b0490bba36fe35ea296305 |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-12-11T17:38:37Z |
| publishDate | 2017-10-01 |
| publisher | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia |
| record_format | Article |
| series | Electronic Journal of Graph Theory and Applications |
| spelling | doaj.art-a290acb3f6b0490bba36fe35ea2963052022-12-22T00:56:35ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872017-10-015210.5614/ejgta.2017.5.2.15101Cofinite graphs and their profinite completionsAmrita Acharyya0Jon M Corson1Bikash Das2Department of Mathematics and Statistics, University of ToledoDepartment of Mathematics, University of AlabamaDepartment of Mathematics, University of North Georgia<p>We generalize the idea of cofinite groups, due to B. Hartley, [2]. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions.</p><p>The idea of constructing a cofinite graph starts with defining a uniform topological graph $\Gamma$, in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over $\Gamma$. It is established that for any cofinite graph there exists a unique cofinite completion.</p>https://www.ejgta.org/index.php/ejgta/article/view/222profinite graph, cofinite graph, profinite group, cofinite group, uniform space, completion, cofinite entourage |
| spellingShingle | Amrita Acharyya Jon M Corson Bikash Das Cofinite graphs and their profinite completions Electronic Journal of Graph Theory and Applications profinite graph, cofinite graph, profinite group, cofinite group, uniform space, completion, cofinite entourage |
| title | Cofinite graphs and their profinite completions |
| title_full | Cofinite graphs and their profinite completions |
| title_fullStr | Cofinite graphs and their profinite completions |
| title_full_unstemmed | Cofinite graphs and their profinite completions |
| title_short | Cofinite graphs and their profinite completions |
| title_sort | cofinite graphs and their profinite completions |
| topic | profinite graph, cofinite graph, profinite group, cofinite group, uniform space, completion, cofinite entourage |
| url | https://www.ejgta.org/index.php/ejgta/article/view/222 |
| work_keys_str_mv | AT amritaacharyya cofinitegraphsandtheirprofinitecompletions AT jonmcorson cofinitegraphsandtheirprofinitecompletions AT bikashdas cofinitegraphsandtheirprofinitecompletions |