As the title,how to solve the following problem:
Problem: Consider the cylinder $$ C=\{(x,y,z)\in\mathbb{R}^3|x^2+y^2=1\} $$ and identify the point $(x,y,z)$ with $(-x,-y,-z)$.Show that the quotient space of $C$ by this equivalence relation can be given a differentiable structure (infinite Mobius band).
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