---
tag: 56J7DSVAZH
kind: concept
name: Indecomposable continuum
msc: [54F15]
specializes: [NJQ196M1WR]
sources:
  - url: https://en.wikipedia.org/wiki/Indecomposable_continuum
same_as:
  wikidata: Q2995675
  wikipedia: Indecomposable continuum
---

## Summary

An indecomposable continuum is a [[continuum|NJQ196M1WR]] that is not the union of two proper subcontinua.
Familiar continua such as arcs, circles and discs are decomposable, so the indecomposable ones are a source of strange examples.
They appear in plane topology, as common boundaries of domains, and in dynamics, as attractors.

## Explanations

### L1 human

The interval $[0, 1]$ is the union of the two smaller pieces $[0, 1/2]$ and $[1/2, 1]$, each a continuum.
An indecomposable continuum cannot be cut up like this: any two smaller continua inside it leave something out.
Pictures of them look like infinitely many strands wound back and forth, such as the Knaster bucket handle.
The [[pseudo-arc|VGCTDCGS6V]] is an extreme case, where every subcontinuum is again indecomposable.