# Lebesgue number lemma

Lebesgue number lemma: For every open cover $\mathcal{U}$ of a compact^{} metric space $X$, there exists a real number $\delta >0$ such that every open ball in $X$ of radius $\delta $ is contained in some element of $\mathcal{U}$.

Any number $\delta $ satisfying the property above is called a Lebesgue number for the covering $\mathcal{U}$ in $X$.

Title | Lebesgue number lemma |
---|---|

Canonical name | LebesgueNumberLemma |

Date of creation | 2013-03-22 13:01:05 |

Last modified on | 2013-03-22 13:01:05 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 5 |

Author | djao (24) |

Entry type | Theorem |

Classification | msc 54E45 |

Defines | Lebesgue number |