# Monthly Archives: December 2011

## möbius doble cover

The set $E=M\ddot{o}\stackrel{\sim}\times I$ is an orientable 3-manifold with boundary. In the illustration we see in orange the möbius band at $\frac{1}{2}$ and a small regular neigbourhood of her removed without her, i.e., if $Q={\cal{N}}(M\ddot{o}\times \frac{1}{2})\smallsetminus (M\ddot{o}\times \frac{1}{2})\subset E$, then which is $E\smallsetminus Q$?

the last step is $M\ddot{o}\times\frac{1}{2}$ in orange, and $M\ddot{o}\stackrel{\sim}\times I$ without $M\ddot{o}\stackrel{\sim}\times (\frac{1}{2}-\varepsilon, \frac{1}{2}+\varepsilon)$, for $\varepsilon=|\varepsilon|\to \frac{1}{2}$