Category:Abstract Geometry

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This category contains results about Abstract Geometry.
Definitions specific to this category can be found in Definitions/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:

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

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