# Does every first countable Lindelöf space have countable spread?

Does every first countable Lindelöf space have countable spread?

What's meaning of countable spread? see the definition of $s(X)$

$$s(X)=\sup\{|Y|:Y\subseteq X \text{ with the subspace topology is discrete}\}+\aleph_0.$$

Countable spread means that $s(X) = \aleph_0$.

Let $X$ be the lexicographically ordered square; then $X$ is compact and first countable, but $s(X)=c(X)=2^\omega$.