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Almost bi-Lipschitz embeddings and almost homogeneous sets. (English) Zbl 1197.54045

In this paper the authors investigate abstract embeddings between metric spaces, Hilbert spaces, and finite-dimensional Euclidean spaces. They identify a new class of almost homogeneous metric spaces, and show that such spaces have almost bi-Lipschitz embeddings into Hilbert spaces. Furthermore they show that any compact subset \(X\) of a Hilbert space with the set \(X-X\) of differences almost homogeneous can be embedded into a finite-dimensional Euclidean space in an almost bi-Lipschitz way. The paper ends with several interesting open problems.

MSC:

54F45 Dimension theory in general topology
57N35 Embeddings and immersions in topological manifolds
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