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Jul 18, 2017 at 7:48 comment added Benoît Kloeckner The second example tells us that a space can be bi-Lipschitz embeddable in the Euclidean plane but have infinite metric dimension (take a tree which looks like an infinite comb), further confirming that the metric dimension is very sensitive to Lipschitz modifications.
Jul 17, 2017 at 8:10 history answered Benoît Kloeckner CC BY-SA 3.0