metrizable space

可度量化

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

Translation evidence: Literature usage

Meaning in context

A topological space whose topology is induced by some metric.

存在一个度量，其诱导拓扑恰为给定拓扑的空间。

Example

The usual circle is metrizable by the restricted Euclidean distance.

Usage and distinctions

A displayed metric is extra data; different metrics may induce the same topology while having different completeness properties.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 2B, Examples; 9E, Comments on metrizability · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第5周10月10日，主要概念：可度量化 · Checked 2026-10-14
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