Hausdorff space

Hausdorff 空间

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

Other names / variants: T2 space

Translation evidence: Literature usage

Meaning in context

A topological space in which any two distinct points have disjoint open neighborhoods.

任意两个不同点都有互不相交的开邻域的拓扑空间。

Example

Any metric space is Hausdorff by taking balls of radius less than half the distance between two points.

Usage and distinctions

Closed singletons alone give T1 separation, which is weaker.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 9A, Definition 9.1 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第3周9月28日，主要概念：Hausdorff 空间 · Checked 2026-10-14
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