interior of a subset

内部

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

Other names / variants: interior

Translation evidence: Literature usage

Meaning in context

The union of all open subsets of the ambient space contained in the given subset.

包含于给定子集的所有开集的并，亦即其最大的开子集。

Example

The interior of [0,1][0,1] in R\mathbb R is (0,1)(0,1).

Usage and distinctions

Interior is relative to the ambient topology; the same interval is all interior when it is the entire ambient space.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 3B, Interior and closure · Checked 2026-10-14

Translation sources

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