Let $\pi : \tilde M\to M$ be a covering map, $K_1, K_2\subset\tilde M$ are two different connected components and there exists such points $x\in K_1, y\in K_2$ that $\pi(x)=\pi(y)$. In other words, $\pi(K_1)\cap\pi(K_2)\neq\varnothing.$
Is it true that in this instance $\pi(K_1)=\pi(K_2)$?
Give me only an answer and a hint, but not full proof. Thanks a lot!