Subplane of affine plane
This term is related to: incidence geometry
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A subplane of an affine plane is a subset of the point-and-line set that is an affine plane with the induced incidence structure satisfying the further condition that two lines are parallel in the subset if and only if they are parallel in the whole affine plane.
Finite Geometries by Peter Dembowski, Chapter 3. Projective and affine planes