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.
an incidence structure, for which the elements of
S is a partial linear space, if the following axioms hold: 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