Formalizing the Gromov-Hausdorff space

08/31/2021

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by   Sébastien Gouëzel, et al.

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The Gromov-Hausdorff space is usually defined in textbooks as "the space of all compact metric spaces up to isometry". We describe a formalization of this notion in the Lean proof assistant, insisting on how we need to depart from the usual informal viewpoint of mathematicians on this object to get a rigorous formalization.