If a homeomorphism $f:R\rightarrow R$ satisfies $f^2=1$, prove that it has at least one fix point.
What if we set $f^n=1$ instead of $f^2=1$?
If a homeomorphism $f:R\rightarrow R$ satisfies $f^2=1$, prove that it has at least one fix point.
What if we set $f^n=1$ instead of $f^2=1$?
HINT: The sets $U=\{x\in\Bbb R:f(x)>x\}$ and $V=\{x\in\Bbb R:f(x)