Partitions of groups and matroids into independent subsets. (English) Zbl 1224.05084

Banakh, Taras; Protasov, Igor

Algebra Discrete Math. 10, No. 1, 1-7 (2010).

Summary: 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.

MSC:

05B35	Combinatorial aspects of matroids and geometric lattices
05A18	Partitions of sets

Keywords:

matroid; partition; independent subset; continuum hypothesis