2000/01/26 by R. B. Breslav, R. Breslav, Anastasia Stavrova +6
Computer Science · Mathematics · #06A11 #54H10 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras #math.GN #msc:06A11 #msc:54H10
paper · pdf · doi:10.48550/arxiv.math/0001148
7 pages, LaTeX 2e
openalex publication_date 2000/01/26 · arxiv created 2000/01/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.