Wijsman convergence

The convergence was defined by Robert Wijsman.

[1] The same definition was used earlier by Zdeněk Frolík.

[2] Yet earlier, Hausdorff in his book Grundzüge der Mengenlehre defined so called closed limits; for proper metric spaces it is the same as Wijsman convergence.

Let (X, d) be a metric space and let Cl(X) denote the collection of all d-closed subsets of X.

For a point x ∈ X and a set A ∈ Cl(X), set A sequence (or net) of sets Ai ∈ Cl(X) is said to be Wijsman convergent to A ∈ Cl(X) if, for each x ∈ X, Wijsman convergence induces a topology on Cl(X), known as the Wijsman topology.