1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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


    User Avatar
    Staff Emeritus
    Science Advisor

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Composition of continuous maps is continuous
  1. Continuous map (Replies: 25)