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.

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

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