T1 space

T1 分离公理

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

Other names / variants: T1 separation

Translation evidence: Literature usage

Meaning in context

A topological space in which every singleton is closed.

每个单点集均为闭集的拓扑空间。

Example

An infinite set with the cofinite topology is T1.

Usage and distinctions

T1 does not imply Hausdorff separation: two nonempty opens in an infinite cofinite space always intersect.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 9B, Observation 9.8; 9E, separation conditions · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第3周9月28日，主要概念：T_{1} 分离公理 · Checked 2026-10-14
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