Locally finite family of subsets
= Locally finite family of subsets
{title2=$(A_i)_{i\in I}$}
A family $(A_i)$ of subsets of a <topological space> is locally finite if every point has a neighbourhood meeting only finitely many of its members. On a compact space such a family has only finitely many nonempty members. For singleton subsets of a <Riemann surface>, this is the condition permitting prescribed poles of a <meromorphic function> without accumulation inside the surface.