regular space

T3 分离公理

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

Other names / variants: regular separation

Translation evidence: Literature usage

Meaning in context

A space in which a point and a disjoint closed subset can be enclosed in disjoint open sets; T1 is not included in this record.

点与不含该点的闭集可用互不相交的开集分开的空间；本条不附加 T1 条件。

Example

Every metric space satisfies this separation property.

Usage and distinctions

Some authors include T1 in regular or T3; the cited syllabus explicitly treats T1 plus T3 separately.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 9E, Comments, separation-condition list, printed pp. 70–71 · 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_{3}，T_{1}+T_{3}=>T_{2} · Checked 2026-10-14
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