Last Updated：2025/11/21

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(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order. / (set theory, order theory, formally) The ordered pair comprising a set and its partial order.

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partially ordered set

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Source Word

partially ordered set

Noun

broadly formal

(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order. / (set theory, order theory, formally) The ordered pair comprising a set and its partial order.

Japanese Meaning

（集合論、順序理論における定義）1. 与えられた部分的順序関係を持つ集合。 / （集合論、順序理論における定義）2. 部分的順序関係とそれに属する集合から構成される順序対。

What is this buttons?

To analyze convergence of directed systems, we considered each partially ordered set as a category.

Google Translation / DeepL Translation

有向系の収束を解析するために、私たちはそれぞれの部分順序が定められた集合を圏として考えた。

Details

Sense（1）

(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order.

Sense（2）

(set theory, order theory, formally) The ordered pair comprising a set and its partial order.

A partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of "≻" and speak of the partially ordered set P.