Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 3-9
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A. I. Oblakova. Isometric embeddings of finite metric spaces. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 3-9. http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a0/
@article{VMUMM_2016_1_a0,
author = {A. I. Oblakova},
title = {Isometric embeddings of finite metric spaces},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {3--9},
year = {2016},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a0/}
}
TY - JOUR
AU - A. I. Oblakova
TI - Isometric embeddings of finite metric spaces
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 2016
SP - 3
EP - 9
IS - 1
UR - http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a0/
LA - ru
ID - VMUMM_2016_1_a0
ER -
%0 Journal Article
%A A. I. Oblakova
%T Isometric embeddings of finite metric spaces
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 3-9
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a0/
%G ru
%F VMUMM_2016_1_a0
It is proved that there exists a metric on the Cantor set such that any finite metric space with the diameter not exceeding 1 and the number of points not exceeding $n$ can be isometrically embedded into it. We also prove that for any $m,n \in \mathbb N$ there exists a Cantor set in $\mathbb R^m$ that isometrically contains all finite metric spaces embedded into $\mathbb R^m$, containing not more than $n$ points, and having the diameter not exceeding $1$. The latter result is proved for a wide class of metrics on $\mathbb R^m$ and in particular for the Euclidean metric.
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[2] Iliadis S.D., Naidoo I., “On isometric embeddings of compact metric spaces of a countable dimension”, Topol. and its Appl., 160:11 (2013), 1284–1291 | DOI | MR | Zbl
