open set

Japanese: open set(英語表記)openset
open set

… Let S be a topological space, A a subset of A, and x a point of S. If any neighborhood of x contains a point of A other than x , then x is called an accumulation point of A. If a neighborhood of x is contained in A , then x is called an interior point of A. If A contains all of its accumulation points, then A is called a closed set. If all of A 's points are interior points of A, then A is called an open set. These concepts are fundamental in the theory of topological spaces, and a topological space can be defined starting from any one of these concepts. …

*Some of the terminology that mentions "open set" is listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

Sを位相空間,Aをその部分集合とし,xSの点とするとき,xの任意の近傍がx以外にAの点を含むならば,xAの集積点accumulation pointといい,xのある近傍がAに含まれるならば,xAの内点という。Aがそれの集積点をすべて含むならばAを閉集合closed setといい,Aの点はすべてそれの内点ならばAを開集合open setという。これらの概念は位相空間論で基本的で,これらの概念のいずれか一つから出発しても位相空間を定義することができる。…

※「open set」について言及している用語解説の一部を掲載しています。

出典|株式会社平凡社世界大百科事典 第2版について | 情報

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