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Subsequential limit : ウィキペディア英語版 | Subsequential limit
In mathematics, a subsequential limit of a sequence is the limit of some subsequence. Every subsequential limit is a cluster point, but not conversely. In first-countable spaces, the two concepts coincide. The supremum of the set of all subsequential limits of some sequence is called the limit superior, or limsup. Similarly, the infimum of such a set is called the limit inferior, or liminf. See limit superior and limit inferior. If (X,d) is a metric space and there is a Cauchy sequence such that there is a subsequence converging to some x, then the sequence also converges to x.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Subsequential limit」の詳細全文を読む
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