Show that there exists a quotient map $S^2 \to S^1 \times S^1$. Do not write an explicit formula.
I don't see how I can turn a sphere into a torus since a torus has a hole in it. I also don't think I can turn the sphere into a closed cylinder first (to connect the two ends of the disks) because the cylinder has "edges" and it wouldn't be continuous to "sharpen" parts of the sphere into these "edges".