---
tag: 0CP5NDD21C
kind: concept
name: First-countable space
aliases: [first-axiom-of-countability]
msc: [54D70]
sources:
  - url: https://en.wikipedia.org/wiki/First-countable_space
    locator: lead section
same_as:
  wikidata: Q926996
  wikipedia: First-countable space
---

## Summary

A topological space is first-countable when each point has a countable family of neighbourhoods that controls all neighbourhoods of the point.
In such spaces, sequences are enough to describe closures and continuity.