\begin{definition}[Definition:Compactification]
Let $\struct {X, \tau_1}$ be a topological space.
Let $\struct {Y, \tau_2}$ be a compact space.
Let $f: X \to Y$ be a topological embedding.
Let $\Img f$ be everywhere dense in $Y$.
Then either $f$ or $\struct {Y, \tau_2}$ may be called a '''compactification''' of $\struct {X, \tau_1}$.
\end{definition}