 The Hausdorff distance "d"H turns the set "K"("M") of all non-empty compact subsets of "M" into a metric space.One can show that "K"("M") is complete if "M" is complete.One can then define the Gromov–Hausdorff distance between any two metric spaces by considering the minimal Hausdorff distance of isometrically embedded versions of the two spaces.