# Composition of continuous maps is continuous

1. Sep 15, 2006

### 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.

2. Sep 15, 2006

### StatusX

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

3. Sep 15, 2006

### fourier jr

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. Sep 15, 2006

### HallsofIvy

Staff Emeritus
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. Sep 15, 2006

### fourier jr

thats what i was getting at. consider f-1[g-1(U)] & it's pretty much done