**metric space**if and only if

(1) | $X$ is a D11: Set |

(2) | $d$ is a D58: Metric on $X$ |

(3) | $\mathcal{T}_d$ is the D444: Metric topology on $X$ with respect to $d$ |

Definition D1107

Metric space

Formulation 0

An D5107: Triple $M = (X, \mathcal{T}_d, d)$ is a **metric space** if and only if

(1) | $X$ is a D11: Set |

(2) | $d$ is a D58: Metric on $X$ |

(3) | $\mathcal{T}_d$ is the D444: Metric topology on $X$ with respect to $d$ |

Children

▶ | D65: Cauchy sequence |

▶ | D4468: Empty metric space |

▶ | D47: Lipschitz map |

▶ | D1224: Set diameter |

▶ | D1400: Set distance |

▶ | D4475: Trivial metric space |

Results

▶ | R708: Reverse triangle inequality for metric |