Convexity in cristallographical lattices |
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Authors: | Jean-Paul Doignon |
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Institution: | (1) Department of Mathematics, Free University of Brussels, Chaussée de la Hulpe 166, 1170 Bruxelles, Belgium |
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Abstract: | A subset of a (cristallographical) lattice n is called convex whenever it is the intersection of the lattice with a convex set of the affine space containing n. We give a characterization of the convex sets which is intrinsic to the lattice and do the same for other related notions, e.g. the boundary of a convex set of n. A statement analogous to Helly's theorem is also proved. |
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