Definition:Continuum/Topology

From ProofWiki
Jump to navigation Jump to search

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$ be both compact and connected in $T$.


Then $H$ is a continuum.


Examples

Closed Real Interval

A closed real interval is a continuum.


Closed Ball

A closed ball is a continuum.


Also see

  • Results about continua in the context of topology can be found here.


Linguistic Note

The plural of continuum is continua, although the technically-erroneous form continuums can occasionally be found.


Sources