Let \((X, d)\) be a metric space, \(S\subseteq X\) a nonempty subset, and \(x\in X\). The distance from \(x\) to \(S\) is \[ \dist(x, S)\coloneqq\inf_{s\in S} d(x, s). \]
Distance from a point to a subset
D-D5G27
D-D5G27
Let \((X, d)\) be a metric space, \(S\subseteq X\) a nonempty subset, and \(x\in X\). The distance from \(x\) to \(S\) is \[ \dist(x, S)\coloneqq\inf_{s\in S} d(x, s). \]