메뉴 건너뛰기




Volumn 155, Issue 14, 2008, Pages 1561-1575

A theorem of Hrushovski-Solecki-Vershik applied to uniform and coarse embeddings of the Urysohn metric space

Author keywords

Coarse embedding; Group of isometries; Hrushovski Solecki Vershik theorem; Uniform convexity; Uniform embedding; Urysohn metric space

Indexed keywords


EID: 45849122777     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2008.03.002     Document Type: Article
Times cited : (15)

References (44)
  • 1
    • 45849112264 scopus 로고    scopus 로고
    • F. Baudier, G. Lancien, Embeddings of locally finite metric spaces into Banach spaces, math/0702266, Proc. Amer. Math. Soc., in press
    • F. Baudier, G. Lancien, Embeddings of locally finite metric spaces into Banach spaces, math/0702266, Proc. Amer. Math. Soc., in press
  • 2
    • 0003271387 scopus 로고    scopus 로고
    • Geometric Nonlinear Functional Analysis, vol. 1
    • Amer. Math. Soc., Providence, RI
    • Benyamini Y., and Lindenstrauss J. Geometric Nonlinear Functional Analysis, vol. 1. Colloquium Publications vol. 48 (2000), Amer. Math. Soc., Providence, RI
    • (2000) Colloquium Publications , vol.48
    • Benyamini, Y.1    Lindenstrauss, J.2
  • 4
    • 0344095602 scopus 로고    scopus 로고
    • The random graph
    • Nešetril J., and Graham R.L. (Eds), Springer
    • Cameron P. The random graph. In: Nešetril J., and Graham R.L. (Eds). The Mathematics of Paul Erdos (1996), Springer 331-351
    • (1996) The Mathematics of Paul Erdos , pp. 331-351
    • Cameron, P.1
  • 5
    • 84966262442 scopus 로고
    • Some more uniformly convex spaces
    • Day M.M. Some more uniformly convex spaces. Bull. Amer. Math. Soc. 47 (1941) 504-507
    • (1941) Bull. Amer. Math. Soc. , vol.47 , pp. 504-507
    • Day, M.M.1
  • 7
    • 0036521933 scopus 로고    scopus 로고
    • Uniform embeddings into Hilbert space and a question of Gromov
    • Dranishnikov A.N., Gong G., Lafforgue V., and Yu G. Uniform embeddings into Hilbert space and a question of Gromov. Canad. Math. Bull. 45 (2002) 60-70
    • (2002) Canad. Math. Bull. , vol.45 , pp. 60-70
    • Dranishnikov, A.N.1    Gong, G.2    Lafforgue, V.3    Yu, G.4
  • 8
    • 51649182994 scopus 로고
    • On a problem of Smirnov
    • Enflo P. On a problem of Smirnov. Ark. Mat. 8 (1969) 107-109
    • (1969) Ark. Mat. , vol.8 , pp. 107-109
    • Enflo, P.1
  • 9
    • 22444452026 scopus 로고    scopus 로고
    • Partial actions of groups and actions of inverse semigroups
    • Exel R. Partial actions of groups and actions of inverse semigroups. Proc. Amer. Math. Soc. 126 (1998) 3481-3494
    • (1998) Proc. Amer. Math. Soc. , vol.126 , pp. 3481-3494
    • Exel, R.1
  • 11
    • 0002874575 scopus 로고
    • Asymptotic invariants of infinite groups
    • Geometric Group Theory, vol. 2. Sussex, 1991, Cambridge Univ. Press, Cambridge
    • Gromov M. Asymptotic invariants of infinite groups. Geometric Group Theory, vol. 2. Sussex, 1991. London Math. Soc. Lect. Note Ser. vol. 182 (1993), Cambridge Univ. Press, Cambridge 1-295
    • (1993) London Math. Soc. Lect. Note Ser. , vol.182 , pp. 1-295
    • Gromov, M.1
  • 12
    • 0003268230 scopus 로고    scopus 로고
    • Metric Structures for Riemannian and Non-Riemannian Spaces
    • Birkhäuser
    • Gromov M. Metric Structures for Riemannian and Non-Riemannian Spaces. Progress in Mathematics vol. 152 (1999), Birkhäuser
    • (1999) Progress in Mathematics , vol.152
    • Gromov, M.1
  • 13
    • 0002302520 scopus 로고    scopus 로고
    • Spaces and questions
    • GAFA 2000, Tel Aviv, 1999 Part I
    • Gromov M. Spaces and questions. GAFA 2000, Tel Aviv, 1999. Geom. Funct. Anal. Special Volume (2000) 118-161 Part I
    • (2000) Geom. Funct. Anal. , vol.Special , pp. 118-161
    • Gromov, M.1
  • 14
    • 0000147699 scopus 로고
    • A topology for free groups and related groups
    • Hall M. A topology for free groups and related groups. Ann. of Math. 52 (1950) 127-139
    • (1950) Ann. of Math. , vol.52 , pp. 127-139
    • Hall, M.1
  • 15
    • 0347843180 scopus 로고    scopus 로고
    • Ultraproducts in analysis
    • Analysis and Logic. Mons, 1997, Cambridge Univ. Press, Cambridge
    • Henson C.W., and Iovino J. Ultraproducts in analysis. Analysis and Logic. Mons, 1997. London Math. Soc. Lecture Note Ser. vol. 262 (2002), Cambridge Univ. Press, Cambridge 1-110
    • (2002) London Math. Soc. Lecture Note Ser. , vol.262 , pp. 1-110
    • Henson, C.W.1    Iovino, J.2
  • 16
    • 23044518051 scopus 로고    scopus 로고
    • Extending partial automorphisms and the profinite topology on free groups
    • Herwig B., and Lascar D. Extending partial automorphisms and the profinite topology on free groups. Trans. Amer. Math. Soc. 352 (2000) 1985-2021
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 1985-2021
    • Herwig, B.1    Lascar, D.2
  • 17
    • 0041796371 scopus 로고
    • The universal separable metric space of Urysohn and isometric embeddings thereof in Banach spaces
    • Holmes M.R. The universal separable metric space of Urysohn and isometric embeddings thereof in Banach spaces. Fund. Math. 140 (1992) 199-223
    • (1992) Fund. Math. , vol.140 , pp. 199-223
    • Holmes, M.R.1
  • 18
    • 0000202689 scopus 로고
    • Extending partial isomorphisms of graphs
    • Hrushovski E. Extending partial isomorphisms of graphs. Combinatorica 12 (1992) 411-416
    • (1992) Combinatorica , vol.12 , pp. 411-416
    • Hrushovski, E.1
  • 20
    • 45849086660 scopus 로고    scopus 로고
    • N.J. Kalton, Coarse and uniform embeddings into reflexive spaces, Quart. J. Math. Oxford., in press
    • N.J. Kalton, Coarse and uniform embeddings into reflexive spaces, Quart. J. Math. Oxford., in press
  • 21
    • 45849112985 scopus 로고    scopus 로고
    • G. Kasparov, G. Yu, The coarse geometric Novikov conjecture and uniform convexity, math.OA/0507599, Adv. Math., in press
    • G. Kasparov, G. Yu, The coarse geometric Novikov conjecture and uniform convexity, math.OA/0507599, Adv. Math., in press
  • 22
    • 45849144130 scopus 로고    scopus 로고
    • A.S. Kechris, Global Aspects of Ergodic Group Actions and Equivalence Relations, preprint, 10 November 2006, 197 pp
    • A.S. Kechris, Global Aspects of Ergodic Group Actions and Equivalence Relations, preprint, 10 November 2006, 197 pp
  • 23
    • 45849128424 scopus 로고    scopus 로고
    • abstract of talk at the Conference on Geometric Linearization of Graphs and Groups, Lausanne, 22-26 January 2007 (accessed 3 January 2007)
    • Lafforgue V. Expanders with no uniform embedding in a uniformly convex Banach space. abstract of talk at the Conference on Geometric Linearization of Graphs and Groups, Lausanne, 22-26 January 2007. http://bernoulli.epfl.ch/graphs/listeConfJanvier.php (accessed 3 January 2007)
    • Expanders with no uniform embedding in a uniformly convex Banach space
    • Lafforgue, V.1
  • 24
    • 45849088900 scopus 로고    scopus 로고
    • A. Leiderman, V. Pestov, M. Rubin, S. Solecki, V.V. Uspenskij (Eds.), Proceedings of the Workshop on the Universal Urysohn Metric Space (Ben-Gurion University of the Negev, 21-24 May 2006), Topology Appl., Special Volume, in press
    • A. Leiderman, V. Pestov, M. Rubin, S. Solecki, V.V. Uspenskij (Eds.), Proceedings of the Workshop on the Universal Urysohn Metric Space (Ben-Gurion University of the Negev, 21-24 May 2006), Topology Appl., Special Volume, in press
  • 25
    • 33646375936 scopus 로고    scopus 로고
    • Remarks on coarse embeddings of metric spaces into uniformly convex Banach spaces
    • Li J., and Wang Q. Remarks on coarse embeddings of metric spaces into uniformly convex Banach spaces. J. Math. Anal. Appl. 320 (2006) 892-901
    • (2006) J. Math. Anal. Appl. , vol.320 , pp. 892-901
    • Li, J.1    Wang, Q.2
  • 26
    • 45849089276 scopus 로고    scopus 로고
    • J. López-Abad, L. Nguyen Van Thé, The oscillation stability problem for the Urysohn sphere: A combinatorial approach, preprint, November 2006, 21 pp., in press
    • J. López-Abad, L. Nguyen Van Thé, The oscillation stability problem for the Urysohn sphere: A combinatorial approach, preprint, November 2006, 21 pp., in press
  • 27
    • 84972547742 scopus 로고
    • Regular embeddings of a graph
    • Maehara H. Regular embeddings of a graph. Pacific J. Math. 107 (1983) 393-402
    • (1983) Pacific J. Math. , vol.107 , pp. 393-402
    • Maehara, H.1
  • 29
    • 52049084890 scopus 로고    scopus 로고
    • M. Megrelishvili, Topological transformation groups: Selected topics, in: Elliott Pearl, (Ed.), Open Problems in Topology, second ed., Elsevier, 2007, in press
    • M. Megrelishvili, Topological transformation groups: Selected topics, in: Elliott Pearl, (Ed.), Open Problems in Topology, second ed., Elsevier, 2007, in press
  • 30
    • 7544239854 scopus 로고    scopus 로고
    • Globalization of confluent partial actions on topological and metric spaces
    • Megrelishvili M., and Schröder L. Globalization of confluent partial actions on topological and metric spaces. Topology Appl. 145 (2004) 119-145
    • (2004) Topology Appl. , vol.145 , pp. 119-145
    • Megrelishvili, M.1    Schröder, L.2
  • 31
    • 45849147805 scopus 로고    scopus 로고
    • J. Melleray, Some geomeric and dynamical properties of the Urysohn space, 2006 preprint, a contribution to the volume [24]
    • J. Melleray, Some geomeric and dynamical properties of the Urysohn space, 2006 preprint, a contribution to the volume [24]
  • 32
    • 24944517991 scopus 로고    scopus 로고
    • Coarse embeddings of metric spaces into Banach spaces
    • Nowak P.W. Coarse embeddings of metric spaces into Banach spaces. Proc. Amer. Math. Soc. 133 (2005) 2589-2596
    • (2005) Proc. Amer. Math. Soc. , vol.133 , pp. 2589-2596
    • Nowak, P.W.1
  • 33
    • 33645142185 scopus 로고    scopus 로고
    • p-spaces and a conjecture of Dranishnikov
    • p-spaces and a conjecture of Dranishnikov. Fund. Math. 189 (2006) 111-116
    • (2006) Fund. Math. , vol.189 , pp. 111-116
    • Nowak, P.W.1
  • 34
    • 45849124318 scopus 로고    scopus 로고
    • Open problems raised at the Concentration Week on Metric Geometry and Geometric Embeddings of Discrete Metric Spaces, URL: http://www.math.tamu.edu/research/workshops/linanalysis/problems.html (accessed on 27 December 2006)
    • Open problems raised at the Concentration Week on Metric Geometry and Geometric Embeddings of Discrete Metric Spaces, URL: http://www.math.tamu.edu/research/workshops/linanalysis/problems.html (accessed on 27 December 2006)
  • 35
    • 34249694372 scopus 로고    scopus 로고
    • Dynamics of Infinite-dimensional Groups: the Ramsey-Dvoretzky-Milman Phenomenon
    • Amer. Math. Soc., Providence, RI
    • Pestov V. Dynamics of Infinite-dimensional Groups: the Ramsey-Dvoretzky-Milman Phenomenon. University Lecture Series vol. 40 (2006), Amer. Math. Soc., Providence, RI
    • (2006) University Lecture Series , vol.40
    • Pestov, V.1
  • 36
    • 0001012216 scopus 로고
    • Universal graphs and universal functions
    • Rado R. Universal graphs and universal functions. Acta Arithm. 9 (1954) 331-340
    • (1954) Acta Arithm. , vol.9 , pp. 331-340
    • Rado, R.1
  • 37
    • 0002291626 scopus 로고
    • On the profinite topology of the free group
    • Ribes L., and Zalesskiǐ P.A. On the profinite topology of the free group. Bull. London Math. Soc. 25 (1993) 37-43
    • (1993) Bull. London Math. Soc. , vol.25 , pp. 37-43
    • Ribes, L.1    Zalesskiǐ, P.A.2
  • 38
    • 10244251313 scopus 로고    scopus 로고
    • Lectures on Coarse Geometry
    • Amer. Math. Soc., Providence, RI
    • Roe J. Lectures on Coarse Geometry. University Lecture Series vol. 31 (2003), Amer. Math. Soc., Providence, RI
    • (2003) University Lecture Series , vol.31
    • Roe, J.1
  • 39
    • 33644937851 scopus 로고    scopus 로고
    • Extending partial isometries
    • Solecki S. Extending partial isometries. Israel J. Math. 150 (2005) 315-332
    • (2005) Israel J. Math. , vol.150 , pp. 315-332
    • Solecki, S.1
  • 40
    • 0001504899 scopus 로고
    • On the group of isometries of the Urysohn universal metric space
    • Uspenskiǐ V.V. On the group of isometries of the Urysohn universal metric space. Comment. Math. Univ. Carolin. 31 (1990) 181-182
    • (1990) Comment. Math. Univ. Carolin. , vol.31 , pp. 181-182
    • Uspenskiǐ, V.V.1
  • 41
    • 45849086659 scopus 로고    scopus 로고
    • V.V. Uspenskij, On subgroups of minimal topological groups, 1998 preprint, later prepublished at math.GN/0004119, a contribution to the volume [24]
    • V.V. Uspenskij, On subgroups of minimal topological groups, 1998 preprint, later prepublished at math.GN/0004119, a contribution to the volume [24]
  • 42
    • 0012964395 scopus 로고    scopus 로고
    • The universal Urysohn space, Gromov's metric triples, and random metrics on the series of positive numbers
    • Vershik A.M. The universal Urysohn space, Gromov's metric triples, and random metrics on the series of positive numbers. Russian Math. Surveys 53 (1998) 921-928
    • (1998) Russian Math. Surveys , vol.53 , pp. 921-928
    • Vershik, A.M.1
  • 43
    • 33750614053 scopus 로고    scopus 로고
    • The universal and random metric spaces
    • Vershik A.M. The universal and random metric spaces. Russian Math. Surveys 356 (2004) 65-104
    • (2004) Russian Math. Surveys , vol.356 , pp. 65-104
    • Vershik, A.M.1
  • 44
    • 45849090047 scopus 로고    scopus 로고
    • A.M. Vershik, Extensions of the partial isometries of the metric spaces and finite approximation of the group of isometries of Urysohn space, preprint, 2005
    • A.M. Vershik, Extensions of the partial isometries of the metric spaces and finite approximation of the group of isometries of Urysohn space, preprint, 2005


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.