Well-graded spaces of valued sets Original Research Article

Well-graded spaces of valued sets and relations are introduced and their properties are investigated. In particular, it is shown that the space of valued partial orders on a finite set is well-graded. This is a generalization of a well-known result of Bogart (J. Math. Soc. 3 (1973) 49). Motivation for these studies comes from media theory (Falmagne, J. Math. Psych. 41 (2) (1997) 129; Discrete Appl. Math., submitted) where well-graded families of usual sets play an important role.