| Title:
|
Bi-Lipschitz embeddings into low-dimensional Euclidean spaces (English) |
| Author:
|
Matoušek, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
31 |
| Issue:
|
3 |
| Year:
|
1990 |
| Pages:
|
589-600 |
| . |
| Category:
|
math |
| . |
| MSC:
|
51K99 |
| MSC:
|
54C25 |
| idZBL:
|
Zbl 0711.54021 |
| idMR:
|
MR1078491 |
| . |
| Date available:
|
2008-06-05T21:45:26Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106892 |
| . |
| Reference:
|
[AM83] Alon N., Milman J.: Embeddings of $l^k_\infty$ in finite dimensional Banach spaces.Israel J. Math 45 (1983), 265-280. MR 0720303 |
| Reference:
|
[Bou85] Bourgain J.: On Lipschitz embedding of finite metric spaces in Hilbert space.Israel J. Math. 52 (1985), 46-52. Zbl 0657.46013, MR 0815600 |
| Reference:
|
[BFM86] Bourgain J., Figiel T., Milman V.: On Hilbertian subspaces of finite metric spaces.Israel J. Math. 55 (1986), 147-152. MR 0868175 |
| Reference:
|
[BMW86] Bourgain J., Milman V., Wolfson H.: On type of metric spaces.Trans. Am. Math. Soc. 294 (1986), 295-317. Zbl 0617.46024, MR 0819949 |
| Reference:
|
[Enf69a] Enflo P.: On a problem of Smironov.Ark. Mat. 8 (1969), 107-109. MR 0415576 |
| Reference:
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| Reference:
|
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| Reference:
|
[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 0102079 |
| Reference:
|
[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. |
| Reference:
|
[JL84] Johnson W., Lindenstrauss J.: Extensions of Lipschitz maps into a Hilbert space.Contemp. Math. 26 (1984), 189-206. MR 0737400 |
| Reference:
|
[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. Zbl 0631.46016, MR 0907694 |
| Reference:
|
[Km64] Kruskal J. B.: Multidimensional scaling by optimizing goodness-of-fit to a nonmetric hypothesis.Psychometrika 29 (1964), 1-27. Zbl 0123.36803, MR 0169712 |
| Reference:
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[Mat85] Mathar R.: The best Euclidian fit to a given distance matrix in prescribed dimension.Lin. Alg. Appl. 6T (1985), 1-6. MR 0787361 |
| Reference:
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[Ma89] Matoušek J.: Lipschitz distance of metric spaces.CSc. degree thesis (in Czech), Charles University 1989. |
| Reference:
|
[MaS66] Mardešić S., Segal J.: A note on polyhedra embeddable in the plane.Michig. Math. J. 33 (1966), 633-638. MR 0199848 |
| Reference:
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[MaS67] Mardešić S., Segal J.: e-mappxngs and generalized manifolds.Michig. Math. J. 14 (1967), 171-182. MR 0211407 |
| Reference:
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[MiS86] Milman V. D., Schechtman G.: Asymptotic theory of finite dimensional normed spaces.LNM 1200, Springer-Verlag 1986. Zbl 0606.46013, MR 0856576 |
| Reference:
|
[Scho38] Schoenberg I. J.: Metric spaces and positive definite functions.Trans. Amer. Math. Soc. 44 (1938), 522-536. Zbl 0019.41502, MR 1501980 |
| Reference:
|
[WW75] Wells J. H., Williams L. R.: Embeddings and extensions in analysis.Springer-Verlag 1975. Zbl 0324.46034, MR 0461107 |
| . |
