Julien Melleray
Abstract
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Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space $\ell^2({\mathbb N})$. The proof is based on a lem
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Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space $\ell^2({\mathbb N})$. The proof is based on a lem
Key concepts: Mathematics, Isometry group, Group (periodic table), Isometry (Riemannian geometry), Separable space, Space (punctuation), Topology (electrical circuits), Hilbert space