open neighborhood

邻域

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

Translation evidence: Literature usage

Meaning in context

An open subset of a topological space containing the specified point.

含指定点的开集；本条采用开邻域约定。

Example

(−1,1)(-1,1) is an open neighborhood of 00 in R\mathbb R.

Usage and distinctions

Some authors allow any set containing an open neighborhood to be called a neighborhood; that broader convention includes [−1,1][-1,1].

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 2E, Neighborhoods and limits · Checked 2026-10-14

Translation sources

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