# uniform structure of a metric space

Let $(X,d)$ be a metric space. There is a natural uniform structure on $X$, which induces the same topology^{} as the metric. We define a subset $V$ of the Cartesian product $X\times X$ to be an entourage if and only if it contains a subset of the form

$$ |

for some $\epsilon $.

Title | uniform structure of a metric space |
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Canonical name | UniformStructureOfAMetricSpace |

Date of creation | 2013-03-22 12:47:18 |

Last modified on | 2013-03-22 12:47:18 |

Owner | n3o (216) |

Last modified by | n3o (216) |

Numerical id | 6 |

Author | n3o (216) |

Entry type | Derivation |

Classification | msc 54E15 |