Partitions of groups and matroids into independent subsets - Banakh, T.; Protasov, I. (Algebra and Discrete Mathematics, 2010)
Can the set R∖{0} be covered by countably many linearly (algebraically) independent subsets over the field Q? We use a matroid approach to show that an answer is ``Yes'' under the Continuum Hypothesis, and ``No'' under its negation.