User:Leigh.Samphier/Matroids/Axiom:Base Axioms (Matroid)

Definition
Let $S$ be a finite set.

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

Definition 1
$\mathscr B$ is said to satisfy the base axiom :

Definition 2
$\mathscr B$ is said to satisfy the base axiom :

Definition 3
$\mathscr B$ is said to satisfy the base axiom :

Definition 4
$\mathscr B$ is said to satisfy the base axiom :

Definition 5
$\mathscr B$ is said to satisfy the base axiom :

Definition 6
$\mathscr B$ is said to satisfy the base axiom :

Definition 7
$\mathscr B$ is said to satisfy the base axiom :