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Partitions of groups and matroids into independent subsets

Taras Banakh, Igor Protasov

Abstract


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.


Keywords


matroid, partition, independent subset

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