  Generalizing the famous 14-set closure-complement Theorem of Kuratowski from
1922, we prove that for a set $X$ endowed with $n$ pairwise comparable
topologies $\tau_1\subset\dots\subset\tau_n$, by repeated application of the
operations of complement and closure in the topologies $\tau_1,\dots,\tau_n$ to
a subset $A\subset X$ we can obtains at most
$2K(n)=2\sum_{i,j=0}^n\binom{i+j}{i}\binom{i+j}{j}$ distinct sets.
