normal space

T4 分离公理

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

Other names / variants: normal separation

Translation evidence: Literature usage

Meaning in context

A space in which any two disjoint closed subsets have disjoint open neighborhoods; T1 is not included here.

任意两个不交闭集均可被不交开集分别包含的空间；本条不附加 T1。

Example

Metric spaces separate disjoint closed sets using their distance functions.

Usage and distinctions

This is topological normality, unrelated to normal subgroups or Gaussian distributions; definitions including T1 are stronger.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 9E, Comments, Exercise 9.24 and separation-condition list · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第3周9月28日，主要概念及常用结论：T_{4}，T_{1}+T_{4}=>T_{3} · Checked 2026-10-14
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