A note on proximity spaces and connection based mereology

-- Representation theorems for systems of regions have been of interest for some time, and various contexts have been used for this purpose: Mormann [17] has demonstrated the fruitfulness of the methods of continuous lattices to obtain a topological representation theorem for his formalisation of Whiteheadian ontological theory of space; similar results have been obtained by Roeper [20]. In this note, we prove a topological representation theorem for a connection based class of systems, using methods and tools from the theory of proximity spaces. The key novelty is a new proximity semantics for connection relations. Keywords -- Proximity space, pointless geometry, mereology, connection relation

• Type: Conference
• Year: 2001
• Where: FOIS
• Authors: Dimiter Vakarelov, Ivo Düntsch, Brandon Bennett
• Keywords: FOIS 2001, FOIS 2008, Proximity Space, Representation Theorem, Topological Representation Theorem