Topological structure of Urysohn universal spaces |
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Authors: | Piotr Niemiec |
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Affiliation: | Jagiellonian University, Institute of Mathematics, ul. ?ojasiewicza 6, 30-348 Kraków, Poland |
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Abstract: | The main aim of the paper is to prove that every nonempty member P of the algebra of subsets of a nontrivial Urysohn space generated by all balls (open and closed) is an l2-manifold of finite homotopy type. An algorithm of finding a polyhedron K such that P and K×l2 are homeomorphic is presented. An alternative proof of the Uspenskij theorem [V.V. Uspenskij, The Urysohn universal metric space is homeomorphic to a Hilbert space, Topology Appl. 139 (2004) 145-149] is given. |
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Keywords: | Urysohn's universal space Ultrahomogeneous spaces Infinite-dimensional manifolds |
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