\begin{definition}[Definition:Immersion]
An '''immersion''' is a map $f: X \to Y$ from one smooth manifold $X$ to another $Y$ such that:
:$d f_x: T_x \left({X}\right) \to T_{f \left({x}\right)} \left({Y}\right)$
is injective.
{{MissingLinks|Link to a page explaining the meanings of $T_x \left({X}\right)$ and $T_{f \left({x}\right)} \left({Y}\right)$.}}
\end{definition}