Definition 8.2.3 (Fattening).label Let $X$ be a set, $d: X \times X \to [0, \infty)$ be a pseudometric, $A \subset X$, and $\eps > 0$, then
\[B(A, \eps) = \bracs{x \in X|d(x, A) < \eps}= \bigcup_{a \in A}B(a, \eps)\]
is the $\eps$-fattening of $A$ with respect to $d$.