I am struggling with the following:
Let $M$ be a manifold and $X$ a vector field on $M$. If $c:I\rightarrow M$ is a maximal integral curve of the vector field $X$. Then there does not exists a compact subset $K\subset M$ suchthat $c(I)\subset K$ whenever $I\neq \mathbb R$ holds.
Can someone give me some tips?