  Let $M$ be an $n$-dimensional Alexandrov space with curvature $\geq 1$, and
let $\{q_1,\cdots,q_k\}$ be any $\frac\pi2$-separated subset in $M$ (i.e. the
distance $|q_iq_j|\geq\frac{\pi}{2}$ for any $i\neq j$). Under the additional
conditions "$|q_iq_j|<\pi$" and "the diameter $\diam(M)\leq \frac\pi2$", we
respectively give the upper bound of $k$ (which depends only on $n$), and we
classify the (topological or geometric) structure of $M$ when $k$ attains the
upper bound.
