Geodesic
A Union of Euclidean Metric Spaces is Euclidean
Discrete analysis (2016) Cet article a éte moissonné depuis la source Scholastica

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Suppose that a metric space $X$ is the union of two metric subspaces $A$ and $B$ that embed into Euclidean space with distortions $D_A$ and $D_B$, respectively. We prove that then $X$ embeds into Euclidean space with a bounded distortion (namely, with distortion at most $7D_A D_B + 2(D_A+D_B)$). Our result settles an open problem posed by Naor. Additionally, we present some corollaries and extensions of this result. In particular, we introduce and study a new concept of an "external bi-Lipschitz extension". In the end of the paper, we list a few related open problems.
Publié le : 
@article{DAS_2016_a5,
     author = {Konstantin Makarychev and Yury Makarychev},
     title = {A {Union} of {Euclidean} {Metric} {Spaces} is {Euclidean}},
     journal = {Discrete analysis},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2016_a5/}
}
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AU  - Yury Makarychev
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JO  - Discrete analysis
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UR  - http://geodesic.mathdoc.fr/item/DAS_2016_a5/
LA  - en
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%A Konstantin Makarychev
%A Yury Makarychev
%T A Union of Euclidean Metric Spaces is Euclidean
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Konstantin Makarychev; Yury Makarychev. A Union of Euclidean Metric Spaces is Euclidean. Discrete analysis (2016). http://geodesic.mathdoc.fr/item/DAS_2016_a5/