I've been working on problems dealing with the Souslin property. A topological space $X$ has the Souslin property if every pairwise disjoint family of non-empty open subsets of $X$ is countable.
I came across this problem, and I am having trouble with formulating a proof.
A metrizable space $X$ has the Souslin property if and only if it has a countable base.
Can anyone help? Thanks in advance!