Orbit space of torus homeomorphic to mobius strip

general-topology

Solution 1:

From your other question it seems that you've figured out how to show that the quotient is a Mobius strip. For sake of completeness, here's the argument in pictorial form (I apologize for the crude drawings.): enter image description here

Regarding the last step, maybe this (even more poorly-drawn) picture would help: enter image description here

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