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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


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    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


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    (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:)
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