On lattices of convex sets in R^n
| dc.creator | Bergman, George M. | |
| dc.date | 2004-09-16 | |
| dc.date.accessioned | 2026-07-07T08:06:28Z | |
| dc.date.available | 2026-07-07T08:06:28Z | |
| dc.description | Properties of several sorts of lattices of convex subsets of R^n are examined. The lattice of convex sets containing the origin turns out, for n>1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of R^n and the lattice of all convex subsets of R^{n-1}. The lattices of arbitrary, of open bounded, and of compact convex sets in R^n all satisfy the same identities, but the last of these is join-semidistributive, while for n>1 the first two are not. The lattice of relatively convex subsets of a fixed set S \subseteq R^n satisfies some, but in general not all of the identities of the lattice of ``genuine'' convex subsets of R^n. | |
| dc.description | 35 pages, to appear in Algebra Universalis, Ivan Rival memorial issue. See also http://math.berkeley.edu/~gbergman/papers | |
| dc.identifier | https://arxiv.org/abs/math/0409288 | |
| dc.identifier | http://arxiv.org/abs/math/0409288 | |
| dc.identifier | Algebra universalis 53 (2005) 357-395 | |
| dc.identifier | doi:10.1007/s00012-005-1934-0 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130618 | |
| dc.subject | Metric Geometry | |
| dc.subject | 52A20 (primary), 06B20, 54H12 (secondary) | |
| dc.title | On lattices of convex sets in R^n | |
| dc.type | text |