ABSTRACT
We choose the canonical projection as a homeomorphism, more precisely its restriction PI to the set of Xl E ] - 4, I [ and its restriction P2 to the set of Xl E ] -1,4 [. Every coordinate transformation (chart change) p;1 0 Pion the next intersection of domains
Ul nU2 ={(xl ,x2 ): -1<xl<l, x 2 eR} is such that
but, after a complete trip round the strip, it is
We immediately see the Jacobian sign is not constant and thus the Mobius band is not orientable.
