Basisaxiome

Sei $\mathcal{B}$ Basissystem eines Matroids $M$. Dann gilt:

(B1) $\mathcal{B} \neq \emptyset$
(B2) $B_{1}, B_{2} \in \mathcal{B}, e \in B_{1} \backslash B_{2} \Rightarrow \exists f \in B_{2} \backslash B_{1} \operatorname{mit}\left(B_{1} \backslash\{e\}\right) \cup\{f\} \in \mathcal{B}$