Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658369 | Topology and its Applications | 2015 | 11 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Alveen Chand, Ittay Weiss,