Last Updated
：2025/12/03
directed set
Noun
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。
（ plural ）
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(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
To define a direct limit, mathematicians often index diagrams by a directed set so that every pair of indices has a common upper bound.
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To define a direct limit, mathematicians often index diagrams by a directed set so that every pair of indices has a common upper bound.
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