The Gromov-Hausdorff distance between the cloud of bounded metric spaces and the cloud containing the real line is infinite, and a criterion for such infinite cloud distances is proved.
Edwards, The Structure of Superspace
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On the Gromov-Hausdorff distance between the cloud of bounded metric spaces and a cloud with nontrivial stabilizer
The Gromov-Hausdorff distance between the cloud of bounded metric spaces and the cloud containing the real line is infinite, and a criterion for such infinite cloud distances is proved.