Rough Isometries of Lipschitz Function Spaces

Details Rough Isometries of Lipschitz Function Spaces Rough Isometries of Lipschitz Function Spaces

2007-10-04

arxiv.org/abs/0710.1109v1

Mathematics

Metric Geometry

21 pages, 3 figures

Scientific paper

We show that rough isometries between metric spaces X, Y can be lifted to the
spaces of real valued 1-Lipschitz functions over X and Y with supremum metric
and apply this to their scaling limits. For the inverse, we show how rough
isometries between X and Y can be reconstructed from structurally enriched
rough isometries between their Lipschitz function spaces.

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