ABSTRACT
The Hausdorff (more precisely, the Hausdorff-Pompeiu) metric topology is the oldest, and probably the most popular hyperspace topology. The Haudorff metric is defined on a metric space and is the main tool to quantify the distance between subsets of the given metric space. Let (X, d) be a metric space. In what follows, given x ∈ X and A ∈ P(X), the distance of x from A, is defined by
d(x,A) = inf{d(x, a) : a ∈ A}, where A ∈ P(X).
