Definition:Abstract Geometry

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

Then $\left({P, L}\right)$ is an abstract geometry iff:

The elements of $P$ are referred to as points.

The elements of $L$ are referred to as 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