Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Bi-Lipschitz embeddings of hyperspaces of compact sets

100%

Tyson J.

Fundamenta Mathematicae

2005

tom 187

nr 3

229-254

We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in $ℝ^{n+1}$; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1]) of the unit interval contains a bi-Lipschitz copy of a certain self-similar doubling series-parallel graph studied by Laakso, Lang-Plaut, and Lee-Mendel-Naor, and consequently admits no bi-Lipschitz embedding into any uniformly convex Banach space. Schori and West proved that K([0,1]) is homeomorphic with the Hilbert cube, while Hohti showed that K([0,1]) is not bi-Lipschitz equivalent with a variety of metric Hilbert cubes.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Tyson J.

1 2005

Wyniki wyszukiwania

Bi-Lipschitz embeddings of hyperspaces of compact sets