  In this paper, we study extremal subsets in $n$-dimensional Alexandrov spaces
with curvature $\ge\kappa$ and diameter $\le D$. We show that the number of
extremal subsets in an Alexandrov space, the Betti number of an extremal
subset, and the volume of an extremal subset are uniformly bounded above by
some constant depending only on $n$, $\kappa$ and $D$. The proof is an
application of essential coverings introduced by T. Yamaguchi.
