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Well defined operations

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data

    Let C(R) be th set of all continuous functions on ℝ and let O be the germs
    of continuous functions at the origin. We have a natural surjective map π : C(R) → O. Define addition and multiplication in O by, [f ] ⊕ [g] = [f + g], [f ] ⊗ [g] = [f g].

    Prove that the above operations are well defined

    ((This means, you must prove that if f ∼ F and g ∼ G, then f + g ∼ F + G and fg ∼ FG.))



    2. Relevant equations



    3. The attempt at a solution

    I have no idea where to even start with this problem. My teacher tends to include problems on homework that do not pertain to his teachings or anything in our text. I have searched the internet to try to find more about how to solve this sort of problem but I cannot find anything. Any help is greatly appreciated.
     
    Last edited: Oct 16, 2011
  2. jcsd
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