Closed discrete subset
= Closed discrete subset
In a plane <domain>, a closed <discrete subset> is exactly a set meeting every <compact subset> in finitely many points. This local finiteness is necessary for a nonzero <holomorphic function> to have the subset as its entire zero set. A merely isolated-point subset can have an accumulation point outside the subset but inside the domain, as $\{1/n:n\geq1\}\subset\mathbb C$ does.
// Destination: analysis.bigb