Open covering - Kaihifuku

… If every element of X belongs to some A _λ , then A is called a covering of X. In this case, if Λ is a finite set, then A is called a finite covering, and if X is a topological space and each A _λ is an open set (or closed set), then A is called an open covering (or closed covering). For example, if n is the set of integers, and we consider the open interval ( n , n +2), then the set of all these is an open covering of the number line R. Similarly, if we consider the closed interval [ n , n +1], then the set of all these is a closed covering of R. …

*Some of the terminology that refers to "open covering" is listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

…Xのどの元もあるA_λに属するならば，をXの被覆という。このとき，Λが有限集合ならばを有限被覆といい，Xが位相空間で各A_λが開集合(または閉集合)ならばを開被覆(または閉被覆)という。例えば，nは整数全体をうごくとして，開区間(n,n＋2)を考えるならば，これらの全体は数直線Rの開被覆となり，同様に，閉区間[n,n＋1]を考えるならば，これらの全体はRの閉被覆となる。…

※「開被覆」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