**empty metric space**if and only if

(1) | $X = \emptyset$ (D13: Empty set) |

(2) | $d$ is an D219: Empty map |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Basic binary operation

▾ Unsigned basic binary operation

▾ Semimetric

▾ Metric

▾ Metric space

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Basic binary operation

▾ Unsigned basic binary operation

▾ Semimetric

▾ Metric

▾ Metric space

Formulation 0

An D548: Ordered pair $M = (X, d)$ is an **empty metric space** if and only if

(1) | $X = \emptyset$ (D13: Empty set) |

(2) | $d$ is an D219: Empty map |