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Compact homogeneity of Uryson’s universal metric space. (English. Russian original) Zbl 0999.54022

Russ. Math. Surv. 55, No. 2, 332-333 (2000); translation from Usp. Mat. Nauk 55, No. 2, 131-132 (2000).
From the text: In one of his last papers P. S. Uryson constructed and studied the universal metric space \((U,\rho)\). A. M. Vershik has observed: “This paper has not been widely noticed, although it deserves to be.” Uryson showed that there exists a complete separable metric space \(U\) having the properties: (1) every separable metric space can be isometrically mapped into \(U\); (2) every isometry of a finite subset of \(\mathcal U\) can be extended to an isometry of the whole of \(U\). Uryson also showed that properties (1) and (2) determine the space U uniquely up to isometry.

MSC:

54E35 Metric spaces, metrizability
54-03 History of general topology
54C25 Embedding
54E50 Complete metric spaces
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