dense subset

稠密

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

Translation evidence: Literature usage

Meaning in context

A subset whose closure equals the entire ambient topological space.

闭包等于整个拓扑空间的子集。

Example

Q\mathbb Q is dense in R\mathbb R.

Usage and distinctions

Density does not imply having positive measure or containing an open interval.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 3B, Interior and closure; 8C, Nets and separability · Checked 2026-10-14

Translation sources

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