# Non-separability of the Lipschitz distance

Non-separability of the Lipschitz distance Let X be a compact metric space and ℳ X $${\mathcal{M}}_X$$ 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 ( ℳ X , d L ) $$\left({\mathcal{M}}_X,{d}_L\right)$$ is not separable when X is a closed interval, or an infinite union of shrinking closed intervals. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pacific Journal of Mathematics for Industry Springer Journals

# Non-separability of the Lipschitz distance

, Volume 7 (1) – Mar 31, 2015
7 pages

/lp/springer_journal/non-separability-of-the-lipschitz-distance-kk2Qr9WnsJ
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Quantitative Finance; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical Modeling and Industrial Mathematics; Math Applications in Computer Science
eISSN
2198-4115
D.O.I.
10.1186/s40736-015-0013-5
Publisher site
See Article on Publisher Site

### Abstract

Let X be a compact metric space and ℳ X $${\mathcal{M}}_X$$ 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 ( ℳ X , d L ) $$\left({\mathcal{M}}_X,{d}_L\right)$$ is not separable when X is a closed interval, or an infinite union of shrinking closed intervals.

### Journal

Pacific Journal of Mathematics for IndustrySpringer Journals

Published: Mar 31, 2015

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