Abstract
L. Teirlinck’s theory characterized projective spaces among singular spaces by an axiom on geometric hyperplanes. That theory is recast here so that it applies to any point-line geometry with a suitable subcollection H of geometric hyperplanes satisfying the Teirlinck axiom. If H can separate points, then all singular subspaces are projective spaces. This axiom affects the associated Veldkamp space VH, and has a lot to do with the ability to embed a point-line space into a projective space.
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