極限點是點列的收斂子列的極限,a是Re中的點列{ae}的極限點的充分必要條件是a的任何鄰域內有{ae}的無窮多項,或等價地,對任意正整數e0,在a的任何鄰域內都有{ae}的下標≥e0的項,點列可以有一個或多個極限點,也可以沒有極限點。若且唯若只有一個極限點時點列收斂,每個有界點列至少有一個極限點。對實數列,為了便於處理某些問題,也把定向發散子列的極限(即±∞)算作極限點,這樣,實數列的極限點就是它的收斂子列或定向發散子列的極限。根據收斂子列原理,實數列{ae}有上(下)界若且唯若{ae}的所有極限點的集合L有上(下)界,並且sup L∈L,inf L∈L,即sup L與inf L也是{ae}的極限點,因而是L的最大元與最小元(可以是+∞或-∞)。在文獻中,聚點與極限點這兩個名稱的使用是混亂的,許多人把數集的聚點稱為極限點,也有一些書籍把數列的極限點稱為數列的聚點。
基本介紹
- 中文名:極限點
- 外文名:limit point
- 所屬學科:數理科學
- 相關概念:極限、拓撲空間、數列、點列等
關於極限
度量空間點列
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極限點的定義
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雙核拓撲會計
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