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Andrej Bauer
Andrej Bauer
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I found a statement in which the hypotheses includedinvolving a $1$-Lipschitz homeohomeomorphism $f:X\to X$ of a compact metric space $X$, with Lipshitz coefficient 1, i.e., a non-expansive map, and I don't know any counterexample tocannot think of an example where $f$ beingis not an isometry. Must it be?

I found a statement in which the hypotheses included a $1$-Lipschitz homeo $f:X\to X$, and I don't know any counterexample to $f$ being an isometry.

I found a statement involving a homeomorphism $f:X\to X$ of a compact metric space $X$, with Lipshitz coefficient 1, i.e., a non-expansive map, and cannot think of an example where $f$ is not an isometry. Must it be?

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Saúl RM
Saúl RM
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Is every 1-Lipschitz homeomorphism $f:X\to X$ from a compact metric space to itself an isometry?

I found a statement in which the hypotheses included a $1$-Lipschitz homeo $f:X\to X$, and I don't know any counterexample to $f$ being an isometry.