Topological Representations of Posets
| dc.creator | Breslav, R. | |
| dc.creator | Stavrova, A. | |
| dc.creator | Zapatrin, R. R. | |
| dc.date | 2000-01-26 | |
| dc.date | 2000-01-28 | |
| dc.date.accessioned | 2026-07-07T04:33:26Z | |
| dc.date.available | 2026-07-07T04:33:26Z | |
| dc.description | Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ for this representation an algebraic dual space $P^*$ was used. Here we extend the theory of algabraic duality for posets generalizing the notion of an ideal. This approach yields a sufficient condition for the collection of clopen subsets of a subset of $P^*$ (with respect to induced closures) to be isomorphic to $P$. Applying this result to certain classes of posets we prove some representation theorems and get a topological characterization of orthocomplementations. | |
| dc.description | 7 pages, LaTeX 2e | |
| dc.identifier | https://arxiv.org/abs/math/0001148 | |
| dc.identifier | http://arxiv.org/abs/math/0001148 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58573 | |
| dc.subject | General Topology | |
| dc.subject | 54H10; 06A11 | |
| dc.title | Topological Representations of Posets | |
| dc.type | text |