Compact Orthoalgebras
| dc.creator | Wilce, Alexander | |
| dc.date | 2004-05-28 | |
| dc.date.accessioned | 2026-07-07T06:09:49Z | |
| dc.date.available | 2026-07-07T06:09:49Z | |
| dc.description | We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove that any compact regular TOA is atomistic, and has a compact center. We prove also that any compact TOA with isolated 0 is of finite height. We then focus on stably ordered TOAs: those in which the upper-set generated by an open set is open. These include both topological orthomodular lattices and interval orthoalgebras -- in particular, projection lattices. We show that the topology of a compact stably-ordered TOA with isolated 0 is determined by that of of its space of atoms. | |
| dc.description | 10 pp., LaTeX 2e. An improved and extended treatment of material from sections 2 and 3 of math.RA/0301072 | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0405180 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0405180 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92088 | |
| dc.subject | Quantum Physics | |
| dc.title | Compact Orthoalgebras | |
| dc.type | text |