English Dictionary

total order

名詞

(set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x).

日本語の意味

全順序：集合上の順序関係の一種で、任意の二つの要素が互いに比較可能である（つまり、任意のx, yに対してx ≤ yまたはy ≤ xが成立する）という性質を持つ順序関係。

If the relation ≤ is a total order on S, then for any x, y ∈ S either x ≤ y or y ≤ x.

関係≤が集合S上の全順序であるならば、任意のx,y∈Sについてx≤yまたはy≤xのいずれかが成り立ちます。

意味（1）

(set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x).

[…] we conclude §2.1 by showing how, given a triangulation 𝛥 (i.e., simplicial decomposition) of a closed oriented 3-manifilld M, and a total order '<' on the set of vertices of 𝛥, as well as a choice of a system ℬ of orthonormal bases for various Hilbert spaces that get specified in the process, we may obtain a complex number ⟨(M,𝛥,<,ℬ)⟩.

total orders （ plural ）