Template-Type: ReDIF-Paper 1.0
Author-Name: Klaus Nehring
Author-Name-First: Klaus
Author-Name-Last: Nehring
Author-Name: Gordon H. Hanson
Author-Name-First: Gordon H.
Author-Name-Last: Hanson
Author-Name: Humberto G. Llavador
Author-Name-First: Humberto G.
Author-Name-Last: Llavador
Author-Workplace-Name: Department of Economics, University of California Davis
Title: A THEORY OF QUALITATIVE SIMILARITY
Abstract: The central result of this paper establishes an isomorphism between two types of mathematical structures: ""ternary preorders"" and ""convex topologies."" The former are characterized by reflexivity, symmetry and transitivity conditions, and can be interpreted geometrically as ordered betweenness relations; the latter are defined as intersection-closed families of sets satisfying an ""abstract convexity"" property. A large range of examples is given.
 As corollaries of the main result we obtain a version of Birkhoff''s representation theorem for finite distributive lattices, and a qualitative version of the representation of ultrametric distances by indexed taxonomic hierarchies.
Length: 29
File-URL: https://repec.dss.ucdavis.edu/files/o5HxDtphgKZ4QsobhzGz4U72/97-10.pdf
File-Format: application/pdf
Number: 85
Classification-JEL: 
KeyWords: 
Creation-Date: 20030107
Handle: RePEc:cda:wpaper:85