Locally finite collection

A collection of subsets of a topological space ${\displaystyle X}$ is said to be locally finite if each point in the space has a neighbourhood that intersects only finitely many of the sets in the collection.^[1]

In the mathematical field of topology, local finiteness is a property of collections of subsets of a topological space. It is fundamental in the study of paracompactness and topological dimension.

Note that the term locally finite has different meanings in other mathematical fields.