Leigh.Samphier/Sandbox/Definition:Base Axiom (Matroid)/Definition 1

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Definition

Let $S$ be a finite set.

Let $\mathscr B$ be a non-empty set of subsets of $S$.


$\mathscr B$ is said to satisfy the base axiom if and only if:

\((\text B 1)\)   $:$     \(\displaystyle \forall B_1, B_2 \in \mathscr B:\) \(\displaystyle x \in B_1 \setminus B_2 \implies \exists y \in B_2 \setminus B_1 : \paren {B_1 \setminus \set x} \cup \set y \in \mathscr B \)             


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