Locally finite collection
= Locally finite collection
{wiki=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\}\\).