Definition:Subcontinuum

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$ be a continuum in $T$.

Let $K \subseteq H$ also be a continuum in $T$.

Then $K$ is a subcontinuum of $H$.

Linguistic Note
The plural of subcontinuum is subcontinua, although the technically-erroneous form subcontinuums can occasionally be found.