\begin{definition}[Definition:Regular Level Set]
Let $M$ be a smooth manifold.
Let $f \in \map {\CC^\infty} M : M \to \R$ be a smooth real-valued function.
Let $p \in M$ be a base point in $M$.
Let $\rd f_p$ be the differential of $f$ at $p$.
Let $c \in \R$.
Let $\map {f^{-1}} c$ be a level set.
Suppose every point of $\map {f^{-1}} c$ is a regular point of $f$:
:$\forall p \in \map {f^{-1}} c : \rd f_p \ne 0$
Then $\map {f^{-1}} c$ is called a '''regular level set'''.
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\end{definition}