Linear spaces with many projective planes (Q1879094)

Projective spaces can be defined as linear spaces with three points on every line, in which every plane is a projective plane. The authors give answers to the question:``How many planes of a linear space need to be projective planes to ensure that the space is a projective space?'' Call a point \(p\) of a linear space projective if every plane through it is a projective plane. If there is a non-empty subset \(M\) of the set of projective points and two points \(a\) and \(b\) such that the linear closure of \(M\cup \{a,b\}\) is the whole space, then the space is a projective space. However, there are \(n\)-dimensional linear spaces, which are not projective spaces, containing an \(n-2\)-dimensional projective space all of whose points are, with one exception, projective.