Abstract.
We assume that in a linear space \( (P, \frak{L}) \) there is a non-empty set M of points with the property that every plane containing a point of M is a projective plane. In section 3 an example is given that in general \( (P, \frak{L}) \) is not a projective space. But if M can be completed by two points to a generating set of P, then \( (P, \frak{L}) \) is a projective space.
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Freitag, R., Kreuzer, A. Linear spaces with many projective planes. J. Geom. 79, 67–74 (2004). https://doi.org/10.1007/s00022-003-1614-1
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DOI: https://doi.org/10.1007/s00022-003-1614-1