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Fibers of a map

  1. Oct 26, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove that the nonempty fibers of a map form a partition of the domain.



    3. The attempt at a solution

    Ok so we have some map phi: S -->T

    And we want to show that its pre-image phi-1(t) = {s in S | phi(s)=t} forms a partition of the domain.

    Im really confused here. I assume that it is talking about that domian of phi which is S (i think) but i have no clue how this preimage forms partitions.
     
    Last edited: Oct 26, 2008
  2. jcsd
  3. Oct 26, 2008 #2
    any thoughts?
     
  4. Oct 26, 2008 #3

    Dick

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    Doesn't phi^(-1)(t) for t in T constitute a set of non-overlapping sets that cover S? Look up partition.
     
  5. Oct 26, 2008 #4
    Well a partition P of S is a subdivision of S into nonoverlapping subsets

    How do you know phi^(-1)(t) for t in T constitute a set of non-overlapping sets that cover S
     
  6. Oct 27, 2008 #5

    morphism

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    Prove it. Can any two fibers that correspond to different elements of T intersect nontrivially? Is there anything in S that doesn't lie in a fiber?
     
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