Axiom:Abstract Geometry Axioms
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Definition
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.