I'm thinking how to prove that a map is not a covering map. For example let $p:\mathbb R_+\to S^1$ be a map defined by $p(\theta)=(\cos(2\pi\theta),\sin(2\pi\theta))$. I'm trying to find a point which doesn't have a neighborhood evenly covered by $p$. I'm thinking about the point $(-1,0)$, am I in correct way?
I need a hand here