\begin{definition}[Definition:Compact Space/Normed Vector Space/Subspace]
Let $M = \struct{X, \norm {\,\cdot\,}}$ be a normed vector space.
Let $K \subseteq X$ be a subset of $X$.
The normed vector subspace $M_K = \struct {K, \norm {\,\cdot\,}_K}$ is '''compact in $M$''' {{iff}} $M_K$ is itself a compact normed vector space.
\end{definition}