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This is from Topology by Munkres:

Let $p:E \to B$ be a covering map. Suppose $U$ is a open set of $B$ that is evenly covered by $p$. Show that if $U$ is connected, then the partition of $p^{-1}(U)$ into slices is unique.

What I've tried so far

I proved that if $\{V_\alpha\}$ is a slice then each $V_\alpha$ is connected, but I don't know what to do next.

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    It's not good form to ask questions in the imperative; ordering us to "show that" something is true. Also, could you give some context? Is this homework? What have you tried so far?2011-05-20
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    Sorry for that, yes it is a homework.I proved that if $\{V_\alpha\}$ is a slice then each $V_\alpha$ is connected,but I don't know what to do next.thanks.2011-05-20
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    do not use comments for that: instead of editing the question to observe that you've explained something in a comment, edit it to explain it in the question itself! :)2011-05-20
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    By the way, the title of your question is quite unrelated to the question.2011-05-20

3 Answers 3