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Thread: Equivalence relation problem

  1. #1
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    Equivalence relation problem

    Define a relation Rf on X as follows.
    ( x1,x2)∈Rf iff f(x1)=f(x2)
    f h
    X→Y→X/Rf

    I should prove that there exists exactly only one function h:y∈Y→X/Rf such that h is bijective, and h.f=quotient function
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  2. #2
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    Quote Originally Posted by phds216 View Post
    Define a relation Rf on X as follows.
    ( x1,x2)∈Rf iff f(x1)=f(x2)
    f h
    X→Y→X/Rf

    I should prove that there exists exactly only one function h:y∈Y→X/Rf such that h is bijective, and h.f=quotient function
    What is "Y"? Isn't that important?
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