具有一致消失非对称性的连续空间的完备化
Completion of continuity spaces with uniformly vanishing asymmetry
摘要：
度量空间的经典柯西完备化（通过柯西序列）以及一致空间的完备化（通过柯西滤子）都依赖于度量空间或一致空间的对称性。对于拟度量空间和拟一致空间，存在着各种不同的非等价完备化，这些完备化通常定义在满足特定完备化存在所需的关键性质的空间的某个子范畴上。一个一致空间的经典滤子完备化可以被改造成一个度量空间的滤子完备化。我们表明，这种完成过滤器推广到连续空间，满足一种形式的对称，我们称之为一致消失的不对称。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
