https://en.wikipedia.org/wiki/Transversality_(mathematics) Question 1: Let $M$ be a compact $n$-dimensional smooth manifold in $\mathbb{R}^{n+1}$, and take a point $p \notin M$. Prove that there is always a line $l_p$ passing through $p$ such that $l_p \cap M \neq \emptyset$, and $l_p$ intersects transversally with $M$. Question 2: Let $M$ be a compact $n$-dimensional smooth manifold in $\mathbb{R}^{n+m}$, and take a point $p \notin M$. Prove that for all $1\leq k\leq m$, there is always a hyper…
