关于概率拟度量空间的注记

1973年， Lawvere引入了强化范畴的Cauchy完备的概念， 并且证明:若把度量空间看成［0,∞］op上的强化范畴，则强化范畴意义下的Cauchy完备和通常由Cauchy序列描述的完备是等价的.本文作者指出在概率拟度量空间中该结论也成立.确切地说，概率拟度量空间的双完备也是强化范畴Cauchy完备的一个特例.

A note on the probabilistic quasi-metric spaces

In 1973, Lawvere introduced the notion of Cauchy complete for (enriched) categories and demonstrated that in the case of metric spaces (viewed as categories enriched over 0,∞]op) this notion is equivalent to the usual complete of metric spaces by Cauchy sequences. In this note it is shown that this is also true for probabilistic quasi-metric spaces. Precisely, the bicomplete of probabilistic quasi-metric spaces is also a special case of Cauchy complete of enriched categories.