Closed subset of projective plane

Definition
A subset of (the point-and-line-set of) a projective plane is said to be closed if it satisfies the following:


 * Given any two points in the subset, the line incident with them is also in the subset
 * Given any two lines in the subset, the point incident with them is also in the subset

Stronger properties

 * Subplane of projective plane
 * Baer subset of projective plane