https://en.wikipedia.org/wiki/Transversality_(mathematics) This problem may be a embarrassed one, but I even could not prove it for the 1 dimensional case. Here is the problem: >**Question 1** $latex M$ is a compact $latex n$-dimensional smooth manifold in $latex R^{n+1}$, take a point $p\notin M$. prove there is always a line $latex l_p$ pass $latex p$ and $latex l_p\cap M\neq \emptyset$, and $latex l_p$ intersect transversally with $latex M$. You can naturally generated it to: >**Qusetio…
