open subset

开集

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

Other names / variants: open set

Translation evidence: Literature usage

Meaning in context

A subset belonging to the specified topology of a space.

属于给定拓扑的子集。

Example

(0,1)(0,1) is open in R\mathbb R, and [0,1)[0,1) is open in the subspace [0,1][0,1].

Usage and distinctions

Openness depends on the ambient space; it does not mean that an interval has two missing endpoints in every context.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

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

Translation sources

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