Index

This illustrates the fact that the cylinder $C$ is homeomorphic to the annulus $A$, where \begin{align*} C &= \{(x,y,z)\in\mathbb{R}^3\;|\;x^2+y^2=1,\quad -1\leq z\leq 1\} \\ A &= \{(x,y)\in\mathbb{R}^2 \;|\; \tfrac{1}{2} \leq \sqrt{x^2+y^2} \leq \tfrac{3}{2} \} \end{align*} A homeomorphism $f\colon C\to A$ is given by $$f(x,y,z) = ((1+z/2)x,\;(1+z/2)y).$$