A = { (x1 , x2) : 0<= x1<=1 and 0<= x2<=1}
B = { (y1, ,y2, y3) : (y1)^2 + (y2)^2 = 1 and 0<= y3<=1}
each with the usual toplogy.
Let f: A--->B be the funtion given by f(x1,x2) = (cos(2pi x1),sin (2pi x1), x2)
How do i give the explicit definition of the equivalence relation ~ on A ?
Any help is greatly apprecitated.
I am trying to prove that there is an equivalence relation on A such that f induces a homeomorphism F: A/~ ---> B.
Once i have worked out what the explicit definition for the equivalence relation ~ on A is i can then go on to:
. prove that f induces a bijection F: A/~ ---> B
. then prove that F is continuous
. then finally prove that F is a homeomorphism.