Bogatyi, S. A. 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. Cited in 1 ReviewCited in 3 Documents MSC: 54E35 Metric spaces, metrizability 54-03 History of general topology 54C25 Embedding 54E50 Complete metric spaces PDFBibTeX XMLCite \textit{S. A. Bogatyi}, Russ. Math. Surv. 55, No. 2, 131--132 (2000; Zbl 0999.54022); translation from Usp. Mat. Nauk 55, No. 2, 131--132 (2000) Full Text: DOI