ABSTRACT
Example: Let M denote a Möbius band in R3. The normal bundle of M in R3 can be visualized by looking at the part of the bundle over the middle circle of M: this part of the bundle is again a Möbius band. One can see this by taking a normal direction (perpendicular to the surface of the Möbius band) at any point and walking around the band along the middle circle. The normal vector will be pointing in the opposite direction. This is not true for the cylinder (S1 × R1). See Möbius band.
