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English
Verb
preordered
- simple past and past participle of preorder
Adjective
preordered (not comparable)
- (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”, in 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.