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. Pacific Journal of Mathematics for Industry Springer Journals

Non-separability of the Lipschitz distance

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Springer Berlin Heidelberg
Copyright © 2015 by Suzuki and Yamazaki; licensee Springer.
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
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