度量空间的完备化空间的等价刻划(英文)

An Alternative Definition of the Completion of Metric Spaces

我们给出了不同于传统的用到稠密性质的对度量空间之完备化空间的定义,并证明此定义与传统定义等价。此定义用范畴论的语言给出,使其可以在任意的范畴中推广。

In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on considerations from category theory, and can be generalized to arbitrary categories.