Axiom:Abstract Geometry Axioms

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Let $P$ be a set.

Let $L$ be a set of subsets of $P$.

$\struct {P, L}$ is an abstract geometry if and only if $\struct {P, L}$ satisfies the axioms:

\((1)\)   $:$     \(\ds \forall A, B \in P: \exists l \in L:\) \(\ds A, B \in l \)      
\((2)\)   $:$     \(\ds \forall l \in L: \exists A, B \in P:\) \(\ds A, B \in l \land A \ne B \)      

These criteria are called the abstract geometry axioms.

Also see