# Heine-Cantor theorem

Let $X,Y$ be uniform spaces, and $f:X\to Y$ a continuous function^{}. If $X$ is compact^{}, then $f$ is uniformly continuous^{}.

For instance, if $f:[a,b]\to \mathbb{R}$ is a continuous function, then it is uniformly continuous.

Title | Heine-Cantor theorem |
---|---|

Canonical name | HeineCantorTheorem |

Date of creation | 2013-03-22 12:45:32 |

Last modified on | 2013-03-22 12:45:32 |

Owner | n3o (216) |

Last modified by | n3o (216) |

Numerical id | 9 |

Author | n3o (216) |

Entry type | Theorem |

Classification | msc 46A99 |