The paper proves d_GH(Z^2,R^2)=sqrt(2)/2 and d_GH(A,R^2)=1/2 for a comb-shaped set A, using a new theorem that bounds GH distance below via r-disjoint covers and asymptotic dimension.
155 (2008), 1265–1296
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Calculating Gromov-Hausdorff distance by means of asymptotic dimension
The paper proves d_GH(Z^2,R^2)=sqrt(2)/2 and d_GH(A,R^2)=1/2 for a comb-shaped set A, using a new theorem that bounds GH distance below via r-disjoint covers and asymptotic dimension.