Hausdorff metric

Definitions

1. 1

   In the abstract metric space of all compact subsets of ℝⁿ, given a pair of compact sets A…

   In the abstract metric space of all compact subsets of ℝⁿ, given a pair of compact sets A and B, the Hausdorff metric is h(A,B)= mbox maxρ(A,B),ρ(B,A) where ρ(A,B)= sup _(a∈A) inf _(b∈B),d(a,b), where d is the Euclidean metric in ℝⁿ.

   • The Hausdorff metric topology was first discovered by D. Pompeiu and by F. Hausdorff in 1927. This topology has been used in a number of areas such as function space topologies, approximation theory, and optimisation (see, e.g., 22).

The neighborhood