Subplane of projective plane

Definition
A subplane of a projective plane is a subset of the point and line set that becomes a projective plane with the induced incidence structure. In other words:


 * If two points belong to the subset, so does the line incident with them
 * If two lines belong to the subset, so does the point incident with them
 * The subset contains a quadrangle

Weaker properties

 * Closed subset of projective plane