Composition of continuous maps is continuous

[mikki]

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.

 

[StatusX]

Show that the composition g o f is a continuous transformation.

Who are you talking to? Show some work if you want some help.

 

[fourier jr]

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?

 

[HallsofIvy]

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?

 

[fourier jr]

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