Suchergebnisse

Characterizations of Pasch-Peano spaces. We show that complete convexity spaces (Bryant and Webster, Cantwell) of dimension at least three are convex subsets of real affine spaces. The proof uses an infinite-dimensional analogue of a result of de Groot and de Vries on convex sets in projective spaces.

Any automorphism of a cristallographical lattice is induced by an affinity. We give an elementary proof for this, and also study semi-spaces for the induced convexity and the segment convexity. E.g., we exhibit finite semispaces in lattices.