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Certain Sequences With Compact Closure

机译:紧凑封闭的某些序列

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摘要

This paper deals with a question which is stated by quite simple definitions. A sequence {x_n} in a space X is called a β-sequence if every subsequence of it has a cluster point in X. The closure of the sequence {x_n} means the closure of {x_n: n ∈ ω} in X. Here we consider the question when a β-sequence has compact closure. We give several answers to this question.
机译:本文讨论了一个非常简单的定义所提出的问题。如果空间X中的序列{x_n}的每个子序列在X中都有一个聚类点,则称为β序列。序列{x_n}的闭合表示X中{x_n:n∈ω}的闭合。当β序列具有紧密闭合时,我们考虑这个问题。我们对此问题给出几个答案。

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