closed subset

闭集

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

Other names / variants: closed set

Translation evidence: Literature usage

Meaning in context

A subset whose complement in the specified ambient topological space is open.

在指定拓扑空间中，其补集为开集的子集。

Example

Z\mathbb Z is closed in the usual real line.

Usage and distinctions

A set may be both open and closed; closedness is not the negation of openness.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 3A, Closed sets · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第1周9月14日，主要概念：闭集 · Checked 2026-10-14
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