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Homework Statement
I want to find a bijective function from [0,1] x [0,1] -> D, where D is the closed unit disc.
Homework Equations
The Attempt at a Solution
I have been able to find two continuous surjective functions, but neither is injective. they are [tex]f_1(s,t)=\left((1-s)\cos{(2\pi t)}+s,(1-s)\sin{(2\pi t)}\right)[/tex] and [tex]f_2(s,t)=\left((1-s)\cos{(2\pi t)},(1-s)\sin{(2\pi t)}\right)[/tex]. I can't think of one that is injective, but there should be one because these two spaces are homeomorphic, right?