partially ordered set

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

広義 フォーマル

(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.

日本語の意味

（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。

英語の意味

(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.

このボタンはなに？

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

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。

詳細

意味（1）

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

意味（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. The ordered fields defined earlier are easily seen to be examples of partially ordered sets.

詳細

partially ordered sets （ plural ）