In a lecture we were trying to show a torus $T^{2}_{a,b}$ is homeomorphic to the planar model $I/\thicksim = \left\{ (x,y)| 0 \le x \le 1, 0 \le y \le 1 \right\} $
I need to show,
$\overline{f}([(x,y)]) = (a+b\cos(u))\left(\cos(v)\mathbf{i}+\sin(v)\mathbf{j}\right)+b\sin(u)\mathbf{k}$
is a bijective function. Does it suffice for me to find an inverse function to show bijectivity?
Ok in the lecture to show something is homeomorphic, we needed to show several things but one thing that confused me is how to show bijectivity. Now I know what it means for something to be bijective, but as for showing this, that's another question.
As for recognising answers, how do I do this properly?