Completion of continuity spaces with uniformly vanishing asymmetry

Alveen Chand, Ittay Weiss*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)130-140
Number of pages11
JournalTopology and its Applications
Early online date22 Jan 2015
Publication statusPublished - 5 Mar 2015


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


Dive into the research topics of 'Completion of continuity spaces with uniformly vanishing asymmetry'. Together they form a unique fingerprint.

Cite this