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Anton Petrunin
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Let $S$ be a unit sphere in the Urysohn space $U$$\mathbb{U}$. Is it true that any isometry $S\to S$ can be extended to an isometry $U\to U$$\mathbb{U}\to \mathbb{U}$?

Let $S$ be a unit sphere in the Urysohn space $U$. Is it true that any isometry $S\to S$ can be extended to an isometry $U\to U$?

Let $S$ be a unit sphere in the Urysohn space $\mathbb{U}$. Is it true that any isometry $S\to S$ can be extended to an isometry $\mathbb{U}\to \mathbb{U}$?

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Anton Petrunin
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Sphere in Urysohn space

Let $S$ be a unit sphere in the Urysohn space $U$. Is it true that any isometry $S\to S$ can be extended to an isometry $U\to U$?