Definition 7.2.1 (Distance Between Sets). Let $X$ be a set, $d: X \times X \to [0, \infty)$ be a pseudometric, and $A, B \subset X$, then
\[d(A, B) = \inf_{\substack{a \in A \\ b \in B}}d(a, b)\]
is the distance between $A$ and $B$.
Definition 7.2.1 (Distance Between Sets). Let $X$ be a set, $d: X \times X \to [0, \infty)$ be a pseudometric, and $A, B \subset X$, then
is the distance between $A$ and $B$.