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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Datum:2018
Hauptverfasser: Banakh, Taras, Protasov, Igor
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2018
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Online Zugang: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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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-637
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spelling admjournalluguniveduua-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
baseUrl_str
datestamp_date 2018-04-04T09:14:15Z
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
work_keys_str_mv AT banakhtaras partitionsofgroupsandmatroidsintoindependentsubsets
AT protasovigor partitionsofgroupsandmatroidsintoindependentsubsets
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last_indexed 2025-12-02T15:46:21Z
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