subspace topology

子空间拓扑

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

Other names / variants: relative topology

Translation evidence: Literature usage

Meaning in context

For a subset A of a topological space X, the topology on A consisting of intersections of A with open subsets of X.

对 A⊆XA\subseteq X，由 AA 与 XX 的开集的所有交集构成的拓扑。

Example

[0,1/2)[0,1/2) is relatively open in [0,1][0,1].

Usage and distinctions

Relatively open subsets need not be open in the ambient space.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 3D, Subspaces, printed pp. 26–27 · Checked 2026-10-14

Translation sources

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