Category:Definitions/Abstract Geometries

This category contains definitions related to Abstract Geometries.
Related results can be found in Category:Abstract Geometries.

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

Then $\struct {P, L}$ is an abstract geometry if and only if $\struct {P, L}$ satisfies the abstract geometry 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 $

Pages in category "Definitions/Abstract Geometries"

The following 5 pages are in this category, out of 5 total.

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