Consider some metric spaces, then
[Hausdorff distance][1] and [Gromov-hausdorff convergence][2]

Also, introduce catagorical notation, it may be very useful.


  [1]: http://en.wikipedia.org/wiki/Hausdorff_distance
  [2]: http://en.wikipedia.org/wiki/Gromov-Hausdorff_convergence