discrete topology

离散拓扑

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

Translation evidence: Literature usage

Meaning in context

The topology on a set in which every subset is open.

把集合的全部子集都规定为开集的拓扑。

Example

Every subset of Z\mathbb Z is open in its usual subspace topology.

Usage and distinctions

A subset being discrete is different from the entire ambient space having discrete topology; a discrete subspace need not be closed.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 2B, Examples · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第1周9月14日，常用例子：离散拓扑 · Checked 2026-10-14
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