Sigma-compact space

Summary

A σ-compact space is a topological space that is a countable union of compact subspaces. Euclidean space $\R^n$ is the main example, as the union of the closed balls of radius $n$. Every σ-compact space is Lindelöf, and every locally compact second-countable space is σ-compact. The notion lets compactness arguments run one piece at a time.