Definition:Abstract Geometry

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

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

Lines
The above axioms thus can be phrased in natural language as:


 * $(1): \quad$ For every two points $A, B \in P$ there is a line $l \in L$ such that $A, B \in l$
 * $(2): \quad$ Every line has at least two points