---
tag: 0JEJATBVD7
kind: concept
name: Continuity in R^n
aliases: [continuous-function-of-several-variables, multivariable-continuity]
msc: [26B05]
uses: [0J8Y1NCY0K, 0XPR1E85W0]
sources:
  - url: https://en.wikipedia.org/wiki/Continuous_function
    locator: Continuous functions between metric spaces
---

## Summary

Take a function between subsets of Euclidean spaces, and a point $a$. The function is continuous at this point when small changes of the input near $a$ give small changes of the value.
For a function of several variables, the input can change in all coordinates at once.