Meanings
- participlepastsimple past and past participle of preorder
- not comparablemathematicsEquipped with a preorder.
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 82 more examples
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 30We 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
Cite this entry
preordered. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/preordered
“preordered.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/preordered. Accessed November 3, 2026.
WatkinsX Dictionary, s.v. “preordered,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/preordered.
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