Definition:Locally Finite Set of Subsets

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $\FF$ be a set of subsets of $S$.

Then $\FF$ is locally finite if and only if each element of $S$ has a neighborhood which intersects a finite number of sets in $\FF$.

Sources

• 1955: John L. Kelley: General Topology: Chapter $4$: Embedding and Metrization

• 1975: James R. Munkres: Topology: Chapter $6$: Metrization Theorems and Paracompactness: $\S39$: Local Finiteness

• 1970: Stephen Willard: General Topology: Chapter $6$: Compactness: $\S20$: Paracompactness: Definition $22.2$