Last Updated：2025/12/03

(algebra, set theory) A set equipped with a preorder such that for any two elements a and b there is an element c such that a ≤ c and b ≤ c.

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directed set

Source Word

directed set

Noun

(algebra, set theory) A set equipped with a preorder such that for any two elements a and b there is an element c such that a ≤ c and b ≤ c.

Japanese Meaning

有向集合：前順序が定められた集合であり、任意の2つの要素 a と b に対して、a ≤ c かつ b ≤ c となる要素 c が存在するという性質を持つ集合。

直接極限を定義するために、数学者は図式を任意の2つの要素に共通の上界が存在するような順序が付けられた集合で添字付けすることが多い。

Sense（1）

(algebra, set theory) A set equipped with a preorder such that for any two elements a and b there is an element c such that a ≤ c and b ≤ c.

directed sets

（ plural ）