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Math Help - Fibers

  1. #1
    Senior Member tukeywilliams's Avatar
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    Fibers

    7.  f: A \rightarrow B is a surjective map of sets. We want to prove that  a \sim b if and only if  f(a) = f(b) is an equivalence relation whose equivalence classes are fibers of  f .
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  2. #2
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    Here it is: <br />
\begin{array}{l}<br />
 \left( {\forall x \in A} \right)\left[ {f(x) = f(x)} \right] \\ <br />
 \left[ {f(x) = f(y)\quad  \Rightarrow \quad f(y) = f(x)} \right] \\ <br />
 \left[ {f(x) = f(y)\quad \& \quad f(y) = f(z)\quad  \Rightarrow \quad f(x) = f(z)} \right] \\ <br />
 \end{array}
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