Topological representation of posets
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.
scientific article; zbMATH DE number 203150