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simple past and past participle of preorder examples
not comparable
(set theory, order theory, of a set) Equipped with a preorder. quotations examples
Most of the theory of this section on linear order spaces (and cones) can be generalized to preordered linear spaces (and wedges).
1980, Johann Schröder, Operator Inequalities, Academic Press, page 8
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.
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
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.
1999, Rafael Villarroel-Flores, Equivariant Homotopy Type of Categories and Preordered Sets, University of Minnesota, page 24