1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: The Geometry of Maps (Help)

  1. Jul 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Let D* = [0,1] x [0,1] and define T on D* by T(x*,y*) = (x*y*, x*). Determine the image set D. Is T one-to-one?

    2. Relevant equations

    3. The attempt at a solution

    Okay... So I know it is not one to one, if you take out the point (x=0) then it is one-to-one, so you must be careful with the origin.
    But I don't know how to find the image set D. Because there are two variables in the first component in T x and y*. How do I find D?
  2. jcsd
  3. Jul 18, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    hi der.physika! :smile:

    it's easier if you break D* into two functions

    what is the image of the function that sends (x, y) to (x, xy)?

    (it may help to consider all the (x, 1)s)
  4. Jul 18, 2010 #3

    Okay... I think I found the solution

    by using parametric equations

    (t,0); (1,t); (t,1), (0,t) and plugging them in yields (0,0), (0,0), (t,t), (0,t) which makes it not 1 to 1. So... it gives me the triangle with those vertices. is this correct?
  5. Jul 19, 2010 #4


    User Avatar
    Science Advisor
    Homework Helper

    (just got up :zzz: …)
    That's right! :smile:

    (as you've seen, a short-cut that will work in any "non-folding" case is to simply find where all the corners go to :wink:)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook