Sublattices of complete lattices with continuity conditions
| dc.creator | Wehrung, Friedrich | |
| dc.date | 2005-01-20 | |
| dc.date.accessioned | 2026-07-07T05:16:13Z | |
| dc.date.available | 2026-07-07T05:16:13Z | |
| dc.description | Various embedding problems of lattices into complete lattices are solved. We prove that for any join-semilattice S with the minimal join-cover refinement property, the ideal lattice IdS of S is both algebraic and dually algebraic. Furthermore, if there are no infinite D-sequences in J(S), then IdS can be embedded into a direct product of finite lower bounded lattices. We also find a system of infinitary identities that characterize sublattices of complete, lower continuous, and join-semidistributive lattices. These conditions are satisfied by any (not necessarily finitely generated) lower bounded lattice and by any locally finite, join-semidistributive lattice. Furthermore, they imply M. Erné's dual staircase distributivity. On the other hand, we prove that the subspace lattice of any infinite-dimensional vector space cannot be embedded into any countably complete, countably upper continuous, and countably lower continuous lattice. A similar result holds for the lattice of all order-convex subsets of any infinite chain. | |
| dc.description | To appear in Algebra Universalis | |
| dc.identifier | https://arxiv.org/abs/math/0501325 | |
| dc.identifier | http://arxiv.org/abs/math/0501325 | |
| dc.identifier | Algebra Universalis 53, no. 2-3 (2005) 149--173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73903 | |
| dc.subject | General Mathematics | |
| dc.subject | 06B23, 06B05, 06B15, 06B35, 06C05 | |
| dc.title | Sublattices of complete lattices with continuity conditions | |
| dc.type | text |