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Math Help - locally connected (topology)

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    locally connected (topology)

    Munkres 3.25 exercise 8 says:

    Let p:{X}\rightarrow{Y} be a quotient map. Show that if X is locally connected then Y is locally connected.

    To do this we consider a component C of the open set U of Y. We should show that p^{-1}(C) is a union of components of p^{-1}(U).

    Anybody have any ideas about how to show that p^{-1}(C) is a union of components of p^{-1}(U)?
    Last edited by TXGirl; May 18th 2008 at 01:18 PM.
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