- #1

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_{1}, x

_{2}, x

_{3}, ...} be a metric space with no isolated points.

f: M → M is continuous with f(x

_{n}) = x

_{n+1}, and f(p) = p.

We say f separates if ∃ δ > 0, ∋ for any y and z there is some n with |f

^{n}(y) - f

^{n}(z)| > δ, where f

^{n+1}(y) = f(f

^{n}(y)).

QUESTION: Does f separate?