Let R denote the real numbers.
Let S^2 denote the unit sphere in R^3
Let f: S^2 -> R^4 be defined by f(x,y,z)=(x^2-y^2,xy,yz,zx)
Can we prove that:
f determines a continuous map g: PR^2 -> R^4 where PR^2 is the real projective plane.
g is a homeomorphism onto a topological subspace of R^4