Locally finite collection

A **locally finite collection** of sets is a concept in topology and set theory. A collection of sets \(\mathcal{A}\) is said to be locally finite if, for every point \(x\) in the ambient space (usually a topological space), there exists a neighborhood \(U\) of \(x\) such that \(U\) intersects only finitely many sets in the collection \(\mathcal{A}\).