# Partial linear spaces

### Related pages

Linear spaces
Isomorphisms of partial linear spaces
A partial linear space is an incidence structure which satisfies the following two axioms.

• Any two distinct points are on at most one line.
• Each line has at least two points.

Given two collinear points, p, q, the unique line joining these two points will be denoted by the symbol . Clearly, two distinct lines have at most one common point. Given two distinct but intersecting lines a, b their common point will be denoted by .

Up to isomorphism, we may assume that lines are sets of points and the incidence relation is the incidence relation . Just replace by the set consisting of all point rows, i.e. In this case, we will omit the symbol I, and write just to denote the partial linear space.

Obviously, the dual of an incidence structure is a partial linear space if and only if each two points are on at most one line and there are at least two lines through any given point.

Contributed by Hauke Klein
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