论文标题
几乎使用以原点为中心的球盖几乎是lipschitz
Almost bi--Lipschitz embeddings using covers of balls centred at the origin
论文作者
论文摘要
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.在本文中，我们扩展了此结果，并表明，如果$ x $是Banach空间的子集，那么$ x-X $在原始角度几乎是均匀的，那么$ x $可以以几乎是bi-lipschitz的方式嵌入欧几里得空间中。
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.
