separable space

可分

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

Translation evidence: Literature usage

Meaning in context

A topological space admitting a countable dense subset.

存在可数稠密子集的拓扑空间。

Example

The usual real line is separable because $\mathbb Q$ is countable and dense.

Usage and distinctions

In metric spaces separability is equivalent to second countability, but the equivalence fails for arbitrary topologies.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Anton Petrunin — A minimalist intro to topologyChapter 8C, Nets and separability, printed p. 57 · Checked 2026-10-14

Translation sources

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

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