A question on continuous maps from Möbius to itself – mathoverflow.net

A question on continuous maps from Möbius to itself – mathoverflow.net

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Let $M$ denotes the Möbius strip. Then is it true that For every continuous map $f:M\to M$ there is $x\in M^\circ$ ($x\notin\partial M$) such that $f(f(x))=x$?

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