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C.F.G
C.F.G
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Let $M$ denotes the Möbius strip. Then is it true that

For every continuous map $f:M\to M$ satisfies there is $x\in M^\circ$ ($x\notin\partial M$) such that $f(f(x))=x$?

Let $M$ denotes the Möbius strip. Then is it true that

For every continuous map $f:M\to M$ satisfies there is $x\in M^\circ$ ($x\notin\partial M$) such that $f(f(x))=x$?

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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C.F.G
C.F.G
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A question on continuous maps from Möbius to itself

Let $M$ denotes the Möbius strip. Then is it true that

For every continuous map $f:M\to M$ satisfies there is $x\in M^\circ$ ($x\notin\partial M$) such that $f(f(x))=x$?