hey, i have trouble proving homeomorphisms, i am new to this concept. the problem is:

The circle {(0, x2, x3): (x2-1)^2 + (x3)^2 = 1} lies in the plane x1=0 in R^3. From the quotient space from the square [0,1]x[0,1] contained in R^2, show that this quotient space is homeomorphic to the torus.

work:

so i know the circle has radius 1 and center (0,1,0) and a torus would be a space that is homeomorphic to the subspace of R^3 and can be obtained by rotating the circle around the x3 axis. and identifying the top edge and bottom edge: (s,0)~(s,1), 0<=s<=1 and the left edge with the right edge, (0,t)~(1,t)

can we use the square [0,2pi]x[0,2pi] for this? i dont know how to tie it in into the proof