how can we describe the universal covering space of the Möbius strip?
the Möbius strip is a square $[0,1]\times [0,1]$ with identifications $(0,y)\sim (1,1-y)$.
So my guess is that the universal covering is an infinite strip $\Bbb R\times [0,1]$. How can we describe the map? I am confused by the twist in the Möbius strip.
The Möbius band is the quotient of $ℝ\times [0,1]$ by the map defined by $f(x,y)= (x+1,1-y)$ which generates a freely and proper action on $ℝ\times [0,1]$ this implies that the universal cover of the Möbius band is $ℝ\times [0,1]$