Let be $Y$ a simply connected space. Show that $Y$ doesn't admit covering maps that aren't homeomorphisms, ie, every cover space of $Y$ is trivial ($I\times Y$, with $I$ a discrete space).
So, I know that if $f:X\to Y$ is a cover map and $Y$ is a connected space, then the cardinal of $p^{-1}(y)$, for each $y\in Y$, is constant, and that a homeomorphism between $X$ and $Y$ is a cover maps such that $\# p^{-1}(y)=1$, for every $y\in Y.$
Any idea?