  We define a topological space to be an "SDL space" if the closure of each one
of its strongly discrete subsets is Lindel\"of. After distinguishing this
property from the Lindel\"of property we make various remarks about cardinal
invariants of SDL spaces. For example we prove that $|X| \leq 2^{\chi(X)}$ for
every SDL Urysohn space and that every SDL $P$-space of character $\leq
\omega_1$ is regular and has cardinality $\leq 2^{\omega_1}$. Finally, we
exploit our results to obtain some partial answers to questions about the
cardinality of cellular-Lindel\"of spaces.
