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which is endowed with the sup-norm,
and let $SPM(Z)$ be the unit sphere of $PM(Z)$. In this paper, we shall prove that for all non-degenerate compact metrizable spaces $X$ and $Y$, and for any surjective isometry $T : SPM(X) \to SPM(Y)$, there exists a homeomorphism $\phi : Y \to X$ such that for any metric $d \in SPM(X)$ and for any pair of points $(x,y) \in Y^2$, $T(d)(x,y) = d(\phi(x),\phi(y))$. As a corollary, we can solve a variant of Tingley's problem on spaces of metics.
From: Katsuhisa Koshino [view email]
[v1]
Wed, 24 Jun 2026 08:35:19 UTC (9 KB)
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