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Homework Help: Composition of continuous maps is continuous

  1. Sep 15, 2006 #1
    Suppose that f: D-->R and g: R-->Y are two continuous transfromations, where D, R, and Y are subsets of the plane. Show that the composition
    g o f is a continuous transformation.
  2. jcsd
  3. Sep 15, 2006 #2


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    Homework Helper

    Who are you talking to? Show some work if you want some help.
  4. Sep 15, 2006 #3
    it doesn't take much to prove that. if you just write down the definitions i think you'll have done half the work. what have you tried so far?
  5. Sep 15, 2006 #4


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    What definition of "continuous" are you using? There are several equivalent ones. The most common is "f is continuous if and only if for every open set U in the range, f-1(U) is an open set in the domain. What is (gof)-1?
  6. Sep 15, 2006 #5
    thats what i was getting at. consider f-1[g-1(U)] & it's pretty much done
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