# Category:Abstract Geometry

Let $P$ be a set and $L$ be a set of subsets of $P$.
Then $\left({P, L}\right)$ is an abstract geometry if and only if:
 $(1)$ $:$ $\displaystyle \forall A, B \in P:$ $\displaystyle \exists l \in L: A, B \in l$ $(2)$ $:$ $\displaystyle \forall l \in L:$ $\displaystyle \exists A, B \in P: A, B \in l \land A \ne B$