Topological representation of posets
type: Item
instance of: scholarly article
title: Topological representation of posets
zbMATH Open document ID: 0786.06001
DOI: 10.1007/BF01196093
author: Elias David
published in: Algebra Universalis
publication date: 1993-07-18T00:00:00Z
review text: There is a canonical imbedding of a poset into a complete Boolean lattice and hence into a Boolean lattice. This gives it a representation set of a Boolean space. In this paper it is proved that there are reflective functors from a category of distributive posets to the subcategories of distributive and Boolean lattices, and consequently there is a topological dual equivalence that extends the Stone duality of Boolean lattices.
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06E15
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 203150
zbMATH Keywords: Boolean space
zbMATH Keywords: Boolean lattice
zbMATH Keywords: reflective functors
zbMATH Keywords: topological dual equivalence
zbMATH Keywords: Stone duality
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
cites work: Quotient Frames and Subspaces
cites work: Ideals in Partially Ordered Sets
cites work: Congruence Relations in Semi-Lattices
cites work: Q3852358
description: scientific article; zbMATH DE number 203150