Priestley Duality for Strong Proximity Lattices

In 1937 Marshall Stone extended his celebrated representation theorem for Boolean algebras to distributive lattices. In modern terminology, the representing topological spaces are zero-dimensional stably compact, but typically not Hausdorff. In 1970, Hilary Priestley realised that Stone's topology could be enriched to yield order-disconnected compact ordered spaces. In the present paper, we generalise Priestley duality to a representation theorem for strong proximity lattices. For these a "Stone-type" duality was given in 1995 in joint work between Philipp S

• Type: Journal
• Year: 2006
• Where: ENTCS
• Authors: Mohamed A. El-Zawawy, Achim Jung
• Keywords: Celebrated Representation Theorem, Compact Ordered Spaces, ENTCS 2006, Strong Proximity