Central subsets of Urysohn universal spaces
نویسنده
چکیده
A subset A of a metric space (X, d) is central iff for every Katětov map f : X → R upper bounded by the diameter of X and any finite subset B of X there is x ∈ X such that f(a) = d(x, a) for each a ∈ A ∪ B. Central subsets of the Urysohn universal space U (see introduction) are studied. It is proved that a metric space X is isometrically embeddable into U as a central set iff X has the collinearity property. The Katětov maps of the real line are characterized.
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