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Uspekhi Mat. Nauk, 1998, Volume 53, Issue 5(323), Pages 57–64 (Mi umn69)  

This article is cited in 41 scientific papers (total in 43 papers)

The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers

A. M. Vershik

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

DOI: https://doi.org/10.4213/rm69

Full text: PDF file (204 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1998, 53:5, 921–928

Bibliographic databases:

UDC: 515.512.556
MSC: 54E50, 60Bxx
Received: 01.08.1998

Citation: A. M. Vershik, “The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers”, Uspekhi Mat. Nauk, 53:5(323) (1998), 57–64; Russian Math. Surveys, 53:5 (1998), 921–928

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. R. R. Bikbov, S. K. Nechaev, “Upper estimate of the cardinality of the set of knots generated by one- and two-dimensional braids”, Theoret. and Math. Phys., 120:2 (1999), 985–996  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. E. A. Gorin, “Topological equivalence of Haar measures on compact groups”, Math. Notes, 68:2 (2000), 167–172  mathnet  crossref  crossref  mathscinet  zmath  isi
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    4. Clemens, JD, “Polish metric spaces: Their classification and isometry groups”, Bulletin of Symbolic Logic, 7:3 (2001), 361  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Vladimir Pestov, “Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups”, Isr J Math, 127:1 (2002), 317  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. A. M. Vershik, “Classification of Measurable Functions of Several Variables and Invariantly Distributed Random Matrices”, Funct. Anal. Appl., 36:2 (2002), 93–105  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. S. A. Bogatyi, “Metrically homogeneous spaces”, Russian Math. Surveys, 57:2 (2002), 221–240  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    9. Gao Su, Kechris A.S., On the classification of Polish metric spaces up to isometry, Mem. Amer. Math. Soc., 161, no. 766, 2003, viii+78 pp.  mathscinet  zmath  isi
    10. A. M. Vershik, “Random metric spaces and universality”, Russian Math. Surveys, 59:2 (2004), 259–295  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Megrelishvili, M, “Globalization of confluent partial actions on topological and metric spaces”, Topology and Its Applications, 145:1–3 (2004), 119  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Uspenskij, V, “The Urysohn universal metric space is homeomorphic to a Hilbert space”, Topology and Its Applications, 139:1–3 (2004), 145  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Vershik A.M., “Random and universal metric spaces”, Dynamics and Randomness II, Nonlinear Phenomena and Complex Systems, 10, 2004, 199–228  crossref  mathscinet  zmath  isi
    14. Kondo, T, “Probability distribution of metric measure spaces”, Differential Geometry and Its Applications, 22:2 (2005), 121  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    15. Kojman, M, “Almost isometric embedding between metric spaces”, Israel Journal of Mathematics, 155 (2006), 309  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    16. Gao, S, “Random generations of the countable random graph”, Annals of Pure and Applied Logic, 143:1–3 (2006), 79  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    17. Nesetril, J, “Ramsey classes of topological and metric spaces”, Annals of Pure and Applied Logic, 143:1–3 (2006), 147  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. J. Math. Sci. (N. Y.), 141:6 (2007), 1601–1607  mathnet  crossref  mathscinet  elib
    19. Pestov, V, “The isometry group of the Urysohn space as a Levy group”, Topology and Its Applications, 154:10 (2007), 2173  crossref  mathscinet  zmath  isi  scopus  scopus
    20. Melleray, J, “On the geometry of Urysohn's universal metric space”, Topology and Its Applications, 154:2 (2007), 384  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    21. Nesetril, J, “Metric spaces are Ramsey”, European Journal of Combinatorics, 28:1 (2007), 457  crossref  mathscinet  zmath  isi  scopus  scopus
    22. Andreas Greven, Peter Pfaffelhuber, Anita Winter, “Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees)”, Probab Theory Relat Fields, 2008  crossref  mathscinet  isi  scopus  scopus
    23. Pestov, VG, “A theorem of Hrushovski-Solecki-Vershik applied to uniform and coarse embeddings of the Urysohn metric space”, Topology and Its Applications, 155:14 (2008), 1561  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    24. Uspenskij, VV, “On subgroups of minimal topological groups”, Topology and Its Applications, 155:14 (2008), 1580  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    25. Vershik, AM, “Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space”, Topology and Its Applications, 155:14 (2008), 1618  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    26. Lionel Nguyen Thé, Norbert W. Sauer, “The Urysohn Sphere Is Oscillation Stable”, GAFA Geom funct anal, 2009  crossref  mathscinet  isi  scopus  scopus
    27. P. B. Zatitskiy, F. V. Petrov, “Correction of metrics”, J. Math. Sci. (N. Y.), 181:6 (2012), 867–870  mathnet  crossref
    28. V. I. Bogachev, A. V. Kolesnikov, “The Monge–Kantorovich problem: achievements, connections, and perspectives”, Russian Math. Surveys, 67:5 (2012), 785–890  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. Niemiec P., “Central Points and Measures, and Dense Subsets of Compact Metric Spaces”, Topol. Methods Nonlinear Anal., 40:1 (2012), 161–180  mathscinet  zmath  isi
    30. Biehler H.F., Pfaffelhuber P., “Compact Metric Measure Spaces and Lambda-Coalescents Coming Down From Infinity”, ALEA-Latin Am. J. Probab. Math. Stat., 9:2 (2012), 269–278  mathscinet  zmath  isi
    31. Anatoly M. Vershik, Pavel B. Zatitskiy, Fedor V. Petrov, “Geometry and dynamics of admissible metrics in measure spaces”, centr.eur.j.math, 11:3 (2013), 379  crossref  mathscinet  zmath  isi  scopus  scopus
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    36. Shioya T., Metric Measure Geometry, Gromov's Theory of Convergence and Concentration of Metrics and Measures, Irma Lectures in Mathematics and Theoretical Physics, 25, Eur. Math. Soc., 2016  crossref  mathscinet  zmath  isi
    37. Aksoy A.G., Ibragimov Z., “Convexity of the Urysohn Universal Space”, J. Nonlinear Convex Anal., 17:6, SI (2016), 1239–1247  mathscinet  zmath  isi
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    42. Camerlo R., Marcone A., Ros L.M., “On Isometry and Isometric Embeddability Between Ultrametric Polish Spaces”, Adv. Math., 329 (2018), 1231–1284  crossref  mathscinet  zmath  isi  scopus  scopus
    43. A. S. Pushnyakov, “On the relationships of cluster measures and distributions of distances in compact metric spaces”, Comput. Math. Math. Phys., 58:4 (2018), 612–620  mathnet  crossref  crossref  isi  elib
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