Zur Struktur Geschlitzter Doppelräume

Let (P, $$\mathfrak{G}$$ ,∥ℓ,∥r) be an incidence space with two parallelisms ∥ℓ and ∥r. (P, $$\mathfrak{G}$$ ,∥ℓ,∥r) is called double space [5], if for any two intersecting lines A and B and for any two points a ∃ A, b ∃ B the ℓ-parallel to B through a and the r-parallel to A through b intersect. A double space (P, $$\mathfrak{G}$$ ,∥ol,∥r) is called h1-slit, if (P, $$\mathfrak{G}$$ ) is a slit space [7] with at most one affine plane through every point of P. We show that every h1-slit double space of at least dimension three contains h1-slit double spaces of dimension three. Every h1-slit double space (P, $$\mathfrak{G}$$ , ∥ℓ,∥r) with ∥ℓ ≠ ∥r has dimension three. The h1-slit double spaces of dimension three are characterized.