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- Title
A note on semigroups, groups and geometric lattices.
- Authors
Peter Flor; Peter Gruber
- Abstract
Abstract Let G be a closed, additive semigroup in a Hausdorff topological vector space. Then G is a group if and only if it satisfies natural convexity conditions of algebraic or geometric-topological type. This yields a characterization of the geometric lattices among the discrete, additive semigroups of Euclidean d-space $${\mathbb{E}^{d}}$$ and, more generally, of direct sums of subspaces and lattices in $${\mathbb{E}^{d}}$$.
- Subjects
SEMIGROUPS (Algebra); GROUP theory; VECTOR analysis; HAUSDORFF measures; VECTOR spaces; FUNCTIONAL analysis; CONVEX domains
- Publication
Archiv der Mathematik, 2009, Vol 93, Issue 3, p253
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-009-0029-0