Hi, can someone please explain how the following is true:
"For any $c>0$ the relations
$$(x,y)\sim (x, \,y+ k c)\quad(k\in{\mathbb Z}), \qquad (x,y)\sim \bigl(x+\ell,\,(-1)^\ell y\bigr) \quad(\ell\in{\mathbb Z})$$
define a Klein bottle $K_c$ of "length" $1$ and "width" $c$ as a quotient of the $(x,y)$-plane , and with a rectangle $[0,1]\times[0,c]$ as fundamental domain."
I cannot see how this is the same as the definition I learned which is $(x,0)\sim (x,1)$ and $(0,y)\sim (c,1-y)$. Thank you!
