👉 In mathematics and computer science, a compactible set is an element of a specific class of sets. This concept is used to define compactness in topology, especially for metric spaces. A compactible set is a subset $S$ of a metric space $(X,d)$ such that for any two points $x,y\in X$, there exists some positive real number $\epsilon > 0$ with the property that every point $z \in S$ satisfies: $$d(x,z) <
