Smallest integer $N(\epsilon)$ such that $K\subset \bigcup_{n=1}^{N(\epsilon)}B(x_i,\epsilon)$

Question

In a metric space, a set $K$ is said to be totally bounded if for each $\epsilon>0$ there exist a finite number of balls $B_1,B_2\dots B_{N(\epsilon)}$ with radius $\epsilon$ which covers $K$.

Does the smallest integer $N(\epsilon)$ has a name in literature. Is there any work which studied this integer in literature ?

Answer 1

$N(\epsilon)$ is called a covering number and it is widely studied in literature, because it is used to calculate Minkowski–Bouligand dimension of a fractal.