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. DefinitionLet an incidence structure, for which the elements of are called points and the elements of are called lines. S is a partial linear space, if the following axioms hold:
If there is a unique line incident with every pair of distinct points, then we get a linear space. PropertiesThe De Bruijn–Erdős theorem shows that in any finite linear space which is not a single point or a single line, we have . ExamplesReferences
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