connected space

连通

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

Translation evidence: Literature usage

Meaning in context

A space with no decomposition into two disjoint nonempty open subsets; the empty space is included here.

不能分成两个非空不交开集之并的空间；本条把空空间也视为连通。

Example

[0,1][0,1] is connected; [0,1]∪[2,3][0,1]\cup[2,3] is not.

Usage and distinctions

Connectedness need not imply path connectedness. Petrunin excludes the empty space; this record states its own convention.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 11A, Definitions; 11B, Key statements · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第6周10月17日，主要概念：连通 · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.