---
tag: 03PPNCM9GG
kind: concept
name: Second-countable space
aliases: [second-axiom-of-countability, completely-separable-space]
msc: [54D70]
sources:
  - url: https://en.wikipedia.org/wiki/Second-countable_space
    locator: lead section
same_as:
  wikidata: Q1363919
  wikipedia: Second-countable space
---

## Summary

A topological space is second-countable when its topology has a countable basis.
This condition limits the size of the topology and holds for Euclidean spaces.