Solution
= Solution
Every $K_n$ is closed in the <Hausdorff> ambient space, because it is <compact>. Inside the <compact> space $K_1$, these sets have the <finite intersection property>: a finite <intersection> equals the member with largest index and is nonempty. If the total <intersection> were empty, their open complements would cover $K_1$; a finite <subcover> would contradict that property. Thus
$$
\boxed{\bigcap_nK_n\ne\varnothing}.
$$