product topology

乘积空间

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

Other names / variants: product space

Translation evidence: Literature usage

Meaning in context

A Cartesian product equipped with the coarsest topology making every coordinate projection continuous; basic opens restrict only finitely many coordinates.

在笛卡尔积上赋予使各坐标投射连续的最粗拓扑；基本开集仅限制有限多个坐标。

Example

The product topology on R2\mathbb R^2 is generated by open rectangles.

Usage and distinctions

The Chinese headword names the equipped space; for infinite products, allowing unrestricted open conditions in every coordinate gives the generally finer box topology.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 6A, Product space; Chapter 7G, Product spaces · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第2周9月26日：拓扑基与邻域基，乘积空间，可数公理（上） · Checked 2026-10-14
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