Composition of continuous maps is continuous

  • Thread starter mikki
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  • #1
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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.
 

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  • #2
StatusX
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mikki said:
Show that the composition g o f is a continuous transformation.
Who are you talking to? Show some work if you want some help.
 
  • #3
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mikki said:
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.
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?
 
  • #4
HallsofIvy
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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?
 
  • #5
740
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HallsofIvy said:
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?
thats what i was getting at. consider f-1[g-1(U)] & it's pretty much done
 

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