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Prove that the Gromov-Hausdorff distance between subsets X and Y of some metric space Z is...

Prove that the Gromov-Hausdorff distance between subsets X
and Y of some metric space Z is 0 if and only if X = Y

question related to Topological data analysis 2

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Answer #1

This can also be prove by using the definition of metric space and certain triangle inequalities

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