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In a paper published posthumously, P.S. Urysohn constructed a complete,separable metric space that contains an isometric copy of every completeseparable metric space, nowadays referred to as the Urysohn universal space.Here we study various convexity properties of the Urysohn universal space andshow that it has a finite ball intersection property. We also note that Urysohnuniversal space is not hyperconvex.

Finite Ball Intersection Property of the Urysohn Universal Space