Definition
A metric space (U,d) is called Urysohn universal if it is separable and complete and has the following property:
- given any finite metric space X, any point x in X, and any isometric embedding f : X\{x} → U, there exists an isometric embedding F : X → U that extends f, i.e. such that F(y) = f(y) for all y in X\{x}.
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