closure of a subset

闭包

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

Other names / variants: closure

Translation evidence: Literature usage

Meaning in context

The intersection of all closed subsets of the ambient space containing the given subset.

包含给定子集的所有闭集的交，亦即包含它的最小闭集。

Example

The closure of Q\mathbb Q in R\mathbb R is R\mathbb R.

Usage and distinctions

A point belongs to the closure if every open neighborhood meets the subset; a sequence characterization needs extra hypotheses.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 3B, Interior and closure · Checked 2026-10-14

Translation sources

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