A linear space is a basic structure in incidence geometry.
Intuitively, this rule can be visualized as the property that two straight lines never intersect more than once.
Linear spaces can be seen as a generalization of projective and affine planes, and more broadly, of 2-
In such a situation the linear spaces complying to (L3) are considered as nontrivial and those that do not are trivial.
The table below shows all possible nontrivial linear spaces of five points.
In the second illustration, seven lines connecting seven pairs of points are not drawn.
(See pencil) The De Bruijn–Erdős theorem shows that in any finite linear space