This is an announcement for the paper “Almost bi--Lipschitz embeddings using covers of balls centred at the origin” by Alexandros Margarishttps://arxiv.org/search/math?searchtype=author&query=Margaris%2C+A.
Abstract: In 2010, Olson & Robinson [Transactions of the American Mathematical Society, 362(1), 145-168] introduced the notion of an almost homogeneous metric space and showed that if $X$ is a subset of a Hilbert space such that $X-X$ is almost homogeneous, then $X$ admits almost bi--Lipschitz embeddings into Euclidean spaces. In this paper, we extend this result and we show that if $X$ is a subset of a Banach space such that $X-X$ is almost homogeneous at the origin, then $X$ can be embedded in a Euclidean space in an almost bi--Lipschitz way.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/2001.02607