The Gromov-Hausdorff distance between two compact metric spaces 
and 
is
 |
where the infimum is taken over all metric spaces 
and all distance-preserving maps 
and 
, and 
is the Hausdorff distance
in 
.
It measures how closely 
and 
can be placed inside a common metric
space.
The Gromov-Hausdorff distance is a metric on the isometry classes of compact metric
spaces. In particular, it is zero exactly when 
and 
are isometric.
