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

Relation with other properties

Weaker properties

• Closed subset of projective plane