Abstract Separation Systems

Abstract

Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree structure theorems in graphs, matroids or CW-complexes to, potentially, image segmentation and cluster analysis. This paper is intended as a concise common reference for the basic definitions and facts about abstract separation systems in these and any future papers using this framework.Comment: This is Section 2, considerably expanded, of the predecessor version 4 of this thread. Sections 3-4 on abstract duality have migrated to [8], Section 5 on applications has moved to [9