topological space

拓扑空间

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

Translation evidence: Literature usage

Meaning in context

A pair consisting of a set and a family of subsets containing the empty set and the whole set and closed under arbitrary unions and finite intersections.

集合与其开集族组成的二元组；开集族含空集和全集，并对任意并及有限交封闭。

Example

{∅,{a},{a,b}}\{\varnothing,\{a\},\{a,b\}\} is a topology on {a,b}\{a,b\}.

Usage and distinctions

Hausdorff separation and countability are additional axioms, not part of this definition.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 2A, Definitions, printed p. 17 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第1周9月14日：拓扑公理，拓扑空间中的一些基本概念，度量空间 · Checked 2026-10-14
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