# 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 $\varepsilon=|\varepsilon|\to \frac{1}{2}$

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### One response to “möbius doble cover”

1. prof dr mircea orasanu

the importance of this question as double over or surfaces is approached often and thus posted from by prof dr mircea orasanu and prof drd horia orasanu and that is followed necessary for LAGRANGIAN AND MOBIUS transforms and surfaces appear in a wide variety of physical problems. For example, separation of the Helmholtz or wave equation in circular cylindrical coordinates leads to Bessel’s equation.
• Generating function, integer order, Jn (x)
Although Bessel functions are of interest primarily as solutions of differential equations, it is instructive and convenient to develop them from a completely different approach, that of the generating function. Let us introduce a function of two variables,