Partial order embeddings with convex range
| dc.creator | Hirschorn, James | |
| dc.date | 2007-01-17 | |
| dc.date.accessioned | 2026-07-07T07:41:32Z | |
| dc.date.available | 2026-07-07T07:41:32Z | |
| dc.description | A careful study is made of embeddings of posets which have a convex range. We observe that such embeddings share nice properties with the homomorphisms of more restrictive categories; for example, we show that every order embedding between two lattices with convex range is a continuous lattice homomorphism. A number of posets are considered; for example, we prove that every product order embedding sigma between the irrationals (i.e. the family of functions from N into N) with convex range is of the form sigma(x)(n) = ((x o g) + y)(n) if n in K, and sigma(x)(n) = y(n) otherwise, for all irrationals x, where K is a subset of N, g:K -> N is a bijection and y is an irrational. The most complex poset examined here is the quotient of the lattice of Baire measurable functions, with codomain of the form N^I for some index set I, modulo equality on a comeager subset of the domain, with its `natural' ordering. | |
| dc.description | 57 pages. Official homepage of this article (preferred preprint there): http://homepage.univie.ac.at/James.Hirschorn/research/embeddings/embeddings.html | |
| dc.identifier | https://arxiv.org/abs/math/0701486 | |
| dc.identifier | http://arxiv.org/abs/math/0701486 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122144 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Logic | |
| dc.subject | 06A06 (Primary) 03E15, 03E40, 06A11, 06B30, 06F05, 54C35 (Secondary) | |
| dc.title | Partial order embeddings with convex range | |
| dc.type | text |