By allowing [infinity] as a distance we have in effect restricted to bounded metric spaces.
On the other hand, in the case of the bounded metric space (A, [d.
A]) be two induced subobjects of the bounded metric space [A.
The Egli-Milner ordering from reflexive sets and the Hausdorff metric from bounded metric spaces can be generalized to sets with similarity as follows:
While in the special case of reflexive sets, the Egli-Milner relation tells us only when a table or an answer is interchangeable with another one, in the special case of bounded metric spaces, the Hausdorff metric allows a more fine-grained control of relaxation.