Last Updated :2025/11/23

open set

Noun
Japanese Meaning
トポロジーにおける「開集合」とは、任意の点からどの方向に微小な移動をしても、その点が所属する集合の内部に留まる性質を持つ集合を指し、境界を含まない円などが例として挙げられる。
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位相空間では、どの点からも十分小さな量だけ任意の方向に動かしてもその点が集合内にとどまるような集合を開集合と呼びます。

plural

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(topology) Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.

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open set

In topology, an open set is a collection of points such that every point has a neighborhood entirely contained within the collection.

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In topology, an open set is a collection of points such that every point has a neighborhood entirely contained within the collection.

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