---
tag: 0VGFHTM75Y
kind: concept
name: Continuous map
aliases: [continuous-function]
msc: [54C05]
sources:
  - url: https://en.wikipedia.org/wiki/Continuous_function
    locator: lead section
---

## Summary

A continuous map is a function that sends nearby points to nearby points.
Between topological spaces, this means that preimages of open sets are open. Between metric spaces, it is the same as the epsilon-delta condition.