# Partial linear space

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.

## Definition

Let $S=({\mathcal P},{\mathcal B}, \textbf{I})$ an incidence structure, for which the elements of ${\mathcal P}$ are called points and the elements of ${\mathcal B}$ are called lines. S is a partial linear space, if the following axioms hold:

• any line is at least incident with two points
• any pair of distinct points is incident with at most one line