 CIN!:   Each descending sequence of inhabited closed located subsets of a compact metric space with at most one common point has inhabited intersection (Cantor’s intersection theorem with uniqueness.) Note that a subset \(S\) of a metric space \((X,\rho)\) is located if for each \(x\) in \(X\) the infimum distance from \(x\) to \(S\) exists. 