Definition:Continuum (Topology)

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.

Also see

• Definition:Subcontinuum
• Definition:Proper Subcontinuum

• Results about continua can be found here.

Linguistic Note

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

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness: Biconnectedness and Continua