## Abstract

The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in question. For qausi-metric spaces and quasi-uniform spaces various non-equivalent completions exist, often defined on a certain subcategory of spaces that satisfy a key property required for the particular completion to exist. The classical filter completion of a uniform space can be adapted to yield a filter completion of a metric space. We show that this completion by filters generalizes to continuity spaces that satisfy a form of symmetry which we call uniformly vanishing asymmetry.

Original language | English |
---|---|

Pages (from-to) | 130-140 |

Number of pages | 11 |

Journal | Topology and its Applications |

Volume | 183 |

Early online date | 22 Jan 2015 |

DOIs | |

Publication status | Published - 5 Mar 2015 |

## Keywords

- Completion
- Continuity space
- Generalized metric
- Quantale
- Quasi-metric
- Quasi-uniform space
- Uniform space
- Value quantale