Partitions of groups and matroids into independent subsets
Can the set \(\mathbb{R}\setminus\{0\}\) be covered by countably many linearly (algebraically) independent subsets over the field \(\mathbb{Q}\)? We use a matroid approach to show that an answer is ``Yes'' under the Continuum Hypothesis, and ``No'' under its negation.
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/637 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-6372018-04-04T09:14:15Z Partitions of groups and matroids into independent subsets Banakh, Taras Protasov, Igor matroid, partition, independent subset 05B35, 05A18 Can the set \(\mathbb{R}\setminus\{0\}\) be covered by countably many linearly (algebraically) independent subsets over the field \(\mathbb{Q}\)? We use a matroid approach to show that an answer is ``Yes'' under the Continuum Hypothesis, and ``No'' under its negation. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/637 Algebra and Discrete Mathematics; Vol 10, No 1 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/637/171 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
matroid partition independent subset 05B35 05A18 |
| spellingShingle |
matroid partition independent subset 05B35 05A18 Banakh, Taras Protasov, Igor Partitions of groups and matroids into independent subsets |
| topic_facet |
matroid partition independent subset 05B35 05A18 |
| format |
Article |
| author |
Banakh, Taras Protasov, Igor |
| author_facet |
Banakh, Taras Protasov, Igor |
| author_sort |
Banakh, Taras |
| title |
Partitions of groups and matroids into independent subsets |
| title_short |
Partitions of groups and matroids into independent subsets |
| title_full |
Partitions of groups and matroids into independent subsets |
| title_fullStr |
Partitions of groups and matroids into independent subsets |
| title_full_unstemmed |
Partitions of groups and matroids into independent subsets |
| title_sort |
partitions of groups and matroids into independent subsets |
| description |
Can the set \(\mathbb{R}\setminus\{0\}\) be covered by countably many linearly (algebraically) independent subsets over the field \(\mathbb{Q}\)? We use a matroid approach to show that an answer is ``Yes'' under the Continuum Hypothesis, and ``No'' under its negation. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/637 |
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AT banakhtaras partitionsofgroupsandmatroidsintoindependentsubsets AT protasovigor partitionsofgroupsandmatroidsintoindependentsubsets |
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2024-04-12T06:25:45Z |
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2024-04-12T06:25:45Z |
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1796109210038042624 |