Non-separability of the Lipschitz distance

Kohei Suzuki; Yohei Yamazaki

doi:10.1186/s40736-015-0013-5

Non-separability of the Lipschitz distance

Metric Geometry 2015-09-15 v2

Authors: Kohei Suzuki , Yohei Yamazaki

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Abstract

Let $X$ be a compact metric space and $\mathcal M_X$ be the set of isometry classes of compact metric spaces $Y$ such that the Lipschitz distance $d_L(X,Y)$ is finite. We show that $(\mathcal M_X, d_L)$ is not separable when $X$ is a closed interval, or an infinite union of shrinking closed intervals.

Keywords

lipschitz spaces distance sets general topology

Cite

@article{arxiv.1412.3491,
  title  = {Non-separability of the Lipschitz distance},
  author = {Kohei Suzuki and Yohei Yamazaki},
  journal= {arXiv preprint arXiv:1412.3491},
  year   = {2015}
}