preordered

preordered

1. simple past tense and past participle of preorder

preordered (not comparable)

1. (set theory, order theory, of a set) Equipped with a preorder.
   • 1980, Johann Schröder, Operator Inequalities, Academic Press, page 8,

     Most of the theory of this section on linear order spaces (and cones) can be generalized to preordered linear spaces (and wedges).

   • 1998, Ghanshyam B. Mehta, Chapter 1: Preference and Utility, Salvador Barbera, Peter Hammond, Christian Seidl (editors), Handbook of Utility Theory, Volume 1: Principles, Springer, page 30,

     It can be proved [see Herden (1989a,c, 1990, 1993a,b) and Herden and Mehta (1997a) that a continuous isotone (or strictly isotone) function defined on a closed subset K of a preordered topological space X has a continuous isotone (or strictly isotone) extension to a function g on X if and only if there is a separable system on X which satisfies certain "separation" conditions.

   • 1999, Rafael Villarroel-Flores, Equivariant Homotopy Type of Categories and Preordered Sets, University of Minnesota, page 24,

     We remind the reader that the barycentric subdivision sd(P) of a preordered set P is the poset of chains in P, ordered by inclusion.