---
tag: NJQ196M1WR
kind: concept
name: Continuum
msc: [54F15]
specializes: [0VKD1TP7F3]
sources:
  - url: https://en.wikipedia.org/wiki/Continuum_(topology)
same_as:
  wikidata: Q5165551
  wikipedia: Continuum (topology)
---

## Summary

A continuum is a nonempty [[compact|0TVJZYB6SH]] [[connected|0V032VWTHD]] metric space.
Continua are the objects of continuum theory, a part of topology that studies curves and their wild relatives.
Arcs, circles, discs and spheres are continua, and so are strange sets such as the [[pseudo-arc|VGCTDCGS6V]] and the [[Warsaw circle|17VG475BRV]].

## Explanations

### L1 human

A continuum is a space in one piece that is also closed and bounded, when it sits in a Euclidean space.
The closed interval $[0, 1]$, a circle and a filled square are continua.
Two disjoint closed intervals are not a continuum, since they are not in one piece.
The open interval $(0, 1)$ is not one either, since it is not compact.
Continua can be very strange: some cannot be split into two smaller continua at all.