# bounded

Given a metric space $(X,d)$, a subset $A\subseteq X$ is said to be *bounded* if there is some positive real number $M$ such that $d(x,y)\le M$ whenever $x,y\in A$.

A function $f:X\to Y$ from a set $X$ to a metric space $Y$ is said to be *bounded* if its range is bounded in $Y$.

Title | bounded |
---|---|

Canonical name | Bounded |

Date of creation | 2013-03-22 12:05:11 |

Last modified on | 2013-03-22 12:05:11 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 12 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 54E35 |

Related topic | TotallyBounded |

Related topic | AlternateStatementOfBolzanoWeierstrassTheorem |