# Mobius band gluing construction

Can somebody help me understand how the mobius band can be viewed as $\mathbb{R}\times [0,1]/\sim$ where $(x,y)\sim (x+1,1-y)$?

(also, if somebody can help me with the appropriate tags)

• Do you believe that $[0,1]\times[0,1]/\sim$ is a Mobius band? This corresponds to taking a strip of paper, giving it a half-twist, and gluing the ends together. The only difference is that you have $\mathbb{R} \times[0,1]/\sim$, so the strip of paper keeps wrapping around the Mobius band infinitely many times. – kccu Nov 1 '16 at 22:01
• @kccu: I think your comment would make a nice answer. – MvG Nov 2 '16 at 9:06
• Are you sure this is $y-1$ and not $1-y$? – MvG Nov 2 '16 at 13:57
• you're right- it has been changed – user384354 Nov 2 '16 at 19:20