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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

Thanks

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    Or use that it is a local homeomorphism from a simply connected space, hence there has to be a homeomorphism of cover ing spaces with the real line, and prove that such homeomorphism cannot exist.2012-12-11

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