Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 31 (1990) no. 3, pp. 589-600 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 51K99, 54C25
@article{CMUC_1990_31_3_a18,
     author = {Matou\v{s}ek, Ji\v{r}{\'\i}},
     title = {Bi-Lipschitz embeddings into low-dimensional {Euclidean} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {589--600},
     year = {1990},
     volume = {31},
     number = {3},
     mrnumber = {1078491},
     zbl = {0711.54021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1990_31_3_a18/}
}
TY  - JOUR
AU  - Matoušek, Jiří
TI  - Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1990
SP  - 589
EP  - 600
VL  - 31
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMUC_1990_31_3_a18/
LA  - en
ID  - CMUC_1990_31_3_a18
ER  - 
%0 Journal Article
%A Matoušek, Jiří
%T Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 1990
%P 589-600
%V 31
%N 3
%U http://geodesic.mathdoc.fr/item/CMUC_1990_31_3_a18/
%G en
%F CMUC_1990_31_3_a18
Matoušek, Jiří. Bi-Lipschitz embeddings into low-dimensional Euclidean spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 31 (1990) no. 3, pp. 589-600. http://geodesic.mathdoc.fr/item/CMUC_1990_31_3_a18/

[AM83] Alon N., Milman J.: Embeddings of $l^k_\infty$ in finite dimensional Banach spaces. Israel J. Math 45 (1983), 265-280. | MR

[Bou85] Bourgain J.: On Lipschitz embedding of finite metric spaces in Hilbert space. Israel J. Math. 52 (1985), 46-52. | MR | Zbl

[BFM86] Bourgain J., Figiel T., Milman V.: On Hilbertian subspaces of finite metric spaces. Israel J. Math. 55 (1986), 147-152. | MR

[BMW86] Bourgain J., Milman V., Wolfson H.: On type of metric spaces. Trans. Am. Math. Soc. 294 (1986), 295-317. | MR | Zbl

[Enf69a] Enflo P.: On a problem of Smironov. Ark. Mat. 8 (1969), 107-109. | MR

[Enf69b] Enflo P.: On the nonexistence of uniform homeomorphisms between $L_p$-spaces. Ark. Mat. vol 8 (1969), 103-105. | MR

[FLM77] Figiel T., Lindenstrauss J., Milman V.: The dimension of almost spherical sections of convex bodies. Acta Math. 59 (1977), 53-94. | MR | Zbl

[Gan59] Ganea T.: Comment on embedding of polyhedra in Euclidean spaces. Bull. Acad. Polon. Sci. SOr. Sci. Math. Astronom. Phys. 7 (1959), 27-32. | MR

[Hei88] Heiser W. J.: Multidimensional scaling with least absolute residuals. in: Classification and related methods of data analysis, H. H. Bock ed., North Holland (1988), 455-472.

[JL84] Johnson W., Lindenstrauss J.: Extensions of Lipschitz maps into a Hilbert space. Contemp. Math. 26 (1984), 189-206. | MR

[JLS87] Johnson W. B., Lindenstrauss J., Schechtman G.: On Lipschitz embedding of finite metric spaces in low dimensional normed spaces. in: Geometrical aspects of functional analysis, (J. Lindenstrauss, V. D. Milman eds.), LNM 1267, Springer-Verlag 1987. | MR | Zbl

[Km64] Kruskal J. B.: Multidimensional scaling by optimizing goodness-of-fit to a nonmetric hypothesis. Psychometrika 29 (1964), 1-27. | MR | Zbl

[Mat85] Mathar R.: The best Euclidian fit to a given distance matrix in prescribed dimension. Lin. Alg. Appl. 6T (1985), 1-6. | MR

[Ma89] Matoušek J.: Lipschitz distance of metric spaces. CSc. degree thesis (in Czech), Charles University 1989.

[MaS66] Mardešić S., Segal J.: A note on polyhedra embeddable in the plane. Michig. Math. J. 33 (1966), 633-638. | MR

[MaS67] Mardešić S., Segal J.: e-mappxngs and generalized manifolds. Michig. Math. J. 14 (1967), 171-182. | MR

[MiS86] Milman V. D., Schechtman G.: Asymptotic theory of finite dimensional normed spaces. LNM 1200, Springer-Verlag 1986. | MR | Zbl

[Scho38] Schoenberg I. J.: Metric spaces and positive definite functions. Trans. Amer. Math. Soc. 44 (1938), 522-536. | MR | Zbl

[WW75] Wells J. H., Williams L. R.: Embeddings and extensions in analysis. Springer-Verlag 1975. | MR | Zbl