A partial linear space (also semilinear or near-linear space) is a basic incidence structure in the field of incidence geometry, that carries slightly less structure than a linear space.The notion is equivalent to that of a linear hypergraph.
Let
S=({lP},{lL},bf{I})
{lP}
{lL}
If there is a unique line incident with every pair of distinct points, then we get a linear space.
The De Bruijn–Erdős theorem shows that in any finite linear space
S=({lP},{lL},bf{I})
|l{P}|\leq|l{L}|
Combinatorics of Finite Geometries. Cambridge University Press 1986,, p. 1-22