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1994 | 144 | 2 | 181-193
Tytuł artykułu

Minimal bi-Lipschitz embedding dimension of ultrametric spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that an ultrametric space can be bi-Lipschitz embedded in $ℝ^n$ if its metric dimension in Assouad's sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.
Słowa kluczowe
Rocznik
Tom
144
Numer
2
Strony
181-193
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-03-24
Twórcy
  • Department of Mathematics, P.O. Box 4 (hallituS.A.u 15), Fin-00014 University of Helsinki, Finland, luukkainen@cc.helsinki.fi
  • epartment of Mathematics, Penn State Altoona, Altoona, Pa 16601-3760, U.S.A., hml@math.psu.edu
Bibliografia
  • [1] M. Aschbacher, P. Baldi, E. B. Baum and R. M. Wilson, Embeddings of ultrametric spaces in finite dimensional structures, SIAM J. Algebraic Discrete Methods 8 (1987), 564-577.
  • [2] P. Assouad, Espaces métriques, plongements, facteurs, Thèse de doctorat d'État, Orsay, 1977.
  • [3] P. Assouad, Étude d'une dimension métrique liée à la possibilité de plongements dans $ℝ^n$, C. R. Acad. Sci. Paris Sér. A 288 (1979), 731-734.
  • [4] P. Assouad, Plongements Lipschitziens dans $ℝ^n$, Bull. Soc. Math. France 111 (1983), 429-448.
  • [5] A. Ben-Artzi, A. Eden, C. Foias and B. Nicolaenko, Hölder continuity for the inverse of Ma né's projection, J. Math. Anal. Appl. 178 (1993), 22-29.
  • [6] R. Engelking, Dimension Theory, PWN, Warszawa, and North-Holland, Amsterdam, 1978.
  • [7] K. Falconer, Fractal Geometry, Wiley, Chichester, 1990.
  • [8] J. B. Kelly, Metric inequalities and symmetric differences, in: Inequalities-II, O. Shisha (ed.), Academic Press, New York, 1970, 193-212.
  • [9] J. B. Kelly, Hypermetric spaces and metric transforms, in: Inequalities-III, O. Shisha (ed.), Academic Press, New York, 1972, 149-158.
  • [10] A. Yu. Lemin, On the stability of the property of a space being isosceles, Uspekhi Mat. Nauk 39 (5) (1984), 249-250 (in Russian); English transl.: Russian Math. Surveys 39 (5) (1984), 283-284.
  • [11] A. Yu. Lemin, Isometric imbedding of isosceles (non-Archimedean) spaces in Euclidean spaces, Dokl. Akad. Nauk SSSR 285 (1985), 558-562 (in Russian); English transl.: Soviet Math. Dokl. 32 (1985), 740-744.
  • [12] J. Luukkainen and P. Tukia, Quasisymmetric and Lipschitz approximation of embeddings, Ann. Acad. Sci. Fenn. Ser. A I Math. 6 (1981), 343-367.
  • [13] J. Luukkainen and J. Väisälä, Elements of Lipschitz topology, ibid. 3 (1977), 85-122.
  • [14] G. Michon, Les cantors réguliers, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), 673-675.
  • [15] H. Movahedi-Lankarani, On the inverse of Ma né's projection, Proc. Amer. Math. Soc. 116 (1992), 555-560.
  • [16] H. Movahedi-Lankarani, An invariant of bi-Lipschitz maps, Fund. Math. 143 (1993), 1-9.
  • [17] A. C. M. van Rooij, Non-Archimedean Functional Analysis, Marcel Dekker, New York, 1978.
  • [18] W. H. Schikhof, Ultrametric Calculus, Cambridge University Press, Cambridge, 1984.
  • [19] A. F. Timan, On the isometric mapping of some ultrametric spaces into $L_p$-spaces, Trudy Mat. Inst. Steklov. 134 (1975), 314-326 (in Russian); English transl.: Proc. Steklov Inst. Math. 134 (1975), 357-370.
  • [20] A. F. Timan and I. A. Vestfrid, Any separable ultrametric space can be isometrically imbedded in $l_2$, Funktsional. Anal. i Prilozhen. 17 (1) (1983), 85-86 (in Russian); English transl.: Functional Anal. Appl. 17 (1983), 70-71.
  • [21] J. H. Wells and L. R. Williams, Embeddings and Extensions in Analysis, Springer, Berlin, 1975.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv144i2p181bwm
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