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
=
(
P
,
B
,
I
)
an incidence structure, for which the elements of
P
are called points and the elements of
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
Projective space
Affine space
Polar space
Generalized quadrangle
Generalized polygon
Near polygon
