Let $\displaystyle H=\{(x,y,z)\in\mathbb R^3|x^2+y^2=1+z^2\},$ and $\displaystyle C=\{(x,y,z)\in\mathbb R^3|x^2+y^2=1\}.$ Prove that $\displaystyle H$ and $\displaystyle C$ as subspaces of $\displaystyle \mathbb R^3$ are homeomorph.

How to solve this analytically? I've seen a geometric solution but I don't see how to work it analytically.

Thanks.