  The depth of a topological space $X$ ($g(X)$) is defined as the supremum of
the cardinalities of closures of discrete subsets of $X$. Solving a problem of
Mart\'inez-Ruiz, Ram\'irez-P\'aramo and Romero-Morales, we prove that the
cardinal inequality $|X| \leq g(X)^{L(X) \cdot F(X)}$ holds for every Hausdorff
space $X$, where $L(X)$ is the Lindel\"of number of $X$ and $F(X)$ is the
supremum of the cardinalities of the free sequences in $X$.
