Contents

# Contents

## Definition

Given a topological space $X$, then a set of subsets $\{S_i \subset X\}_{i \in I}$ is countably locally finite or $\sigma$-locally finite if it is a countable union of locally finite sets of subsets.

This property is used in Nagata-Smirnov metrization theorem:

###### Theorem

A topological space $X$ is metrisable if and only if it is regular, Hausdorff and has a countably locally finite base.

## References

Last revised on April 5, 2019 at 18:19:43. See the history of this page for a list of all contributions to it.