Definition:Sigma-Locally Finite Set of Subsets

Definition

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

A $\sigma$-locally finite set of subsets is a set of subsets which is the countable union of locally finite set of subsets.

Also known as

A $\sigma$-locally finite set of subsets is also known as a countably locally finite set of subsets.

Sources

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

• 1970: Stephen Willard: General Topology: Chapter $6$: Compactness: $\S20$: Paracompactness: Definition $20.2$

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