# diameter

Let $A$ a subset of a pseudometric space $(X,d)$. The *diameter* of $A$ is defined to be

$$sup\{d(x,y):x\in A,y\in A\}$$ |

whenever the supremum exists. If the supremum doesn’t exist, diameter of $A$ is defined to be infinite.

Having finite diameter is not a topological invariant^{}.

Title | diameter |
---|---|

Canonical name | Diameter |

Date of creation | 2013-03-22 12:20:36 |

Last modified on | 2013-03-22 12:20:36 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 4 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 54-00 |

Related topic | Pi |