Let $M$ and $N$ be smooth manifolds and let $S$ be a submanifold of $N$ ($\dim S < \dim N$). Let $\mathfrak S$ be a foliation of $S$. We say that a map between $M$ and $N$ is transverse to $\mathfrak S$ if it is transverse to every leaf of $\mathfrak S$.

Now, suppose $f : M \rightarrow N$ is a smooth map transverse to a foliation $\mathfrak S$ of $S$ at a point $x \in M$ ($f(x) \in S$ and $f$ is transverse to the leaf of $\mathfrak S$ passing through $f(x)$ at the point $x \in M$). Is it possible to find a map $g : M \rightarrow N$, arbitrarily close to $f$ in the strong (Whitney) topology, with $g(x) = f(x)$ and such that $g$ is transverse to $\mathfrak S$ at all points of $M$?