totally ordered

短语

释义与例句

adj.
  1. 1.

    That is equipped with a total order, that is a subset of (the ground set of) a partially ordered set whose partial order is a total order with respect to said subset.

    数学

    1976, K. D. Stroyan, W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Harcourt Brace Jovanovich (Academic Press), page 67, (A.2.5) THEOREM If A is a totally ordered ring and if I is a proper order ideal, then A/I is a totally ordered ring (with the operations and order given above).

    G is a transitive group of order automorphisms of a totally ordered set X, θ is a convex G-congruence on the totally ordered set X, ξ is the order type of the totally ordered set X, ◌̅η is the order type of some class Y=xη of the congruence η,