Partial linear space

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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[edit]

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

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