  We prove that every $n$-vertex complete simple topological graph generates at
least $\Omega(n)$ pairwise disjoint $4$-faces. This improves upon a recent
result by Hubard and Suk. As an immediate corollary, every $n$-vertex complete
simple topological graph drawn in the unit square generates a $4$-face with
area at most $O(1/n)$. This can be seen as a topological variant of Heilbronn's
problem for $4$-faces. We construct examples showing that our result is
asymptotically tight. We also discuss the similar problem for $k$-faces with
arbitrary $k\geq 3$.
