Geodesic
Partitions of groups and matroids into independent subsets
Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 1-7.

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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.
Keywords: matroid, independent subset.
Mots-clés : partition 
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Taras Banakh; Igor Protasov. Partitions of groups and matroids into independent subsets. Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 1-7. http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a1/