sequential compactness

列紧

Geometry & Topology · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

The property that every sequence in a space has a subsequence converging to a point of that space.

空间中的任意序列都有收敛到该空间内某点的子序列。

Example

Every sequence in [0,1][0,1] has a convergent subsequence with limit in [0,1][0,1].

Usage and distinctions

Equivalent to open-cover compactness for metric spaces; not an unrestricted equivalence in topology.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 8B, Compactness implies sequential compactness; 8E, converse · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第5周10月12日，主要概念：列紧 · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.