The aim of this paper is to discuss the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of right K-Cauchy net in a quasi-metric space for which the corresponding completeness is equivalent to the sequential completeness. In this way we complete some results of R. A. Stoltenberg, Proc. London Math. Soc. 17 (1967), 226–240, and V. Gregori and J. Ferrer, Proc. Lond. Math. Soc., III Ser., 49 (1984), 36. A discussion on nets defined over ordered or pre-ordered directed sets is also included.

中文翻译：

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拟伪空间中的完整性-一项调查

本文的目的是讨论在拟度量空间的设置中，通过网络或通过滤波器，依次完整性的各种概念与相应的完整性概念之间的关系。在拟度量空间中，我们提出了右K -Cauchy网络的新定义，其对应的完整性等于顺序的完整性。通过这种方式，我们完成了RA Stoltenberg，Proc。的一些结果。伦敦数学。Soc。17（1967），226–240，以及V. Gregori和J. Ferrer，Proc.Natl.Acad.Sci.USA，87：4877-2877。nd 数学。Soc。，III Ser。，49（1984），36.还讨论了在有序或有序有向集上定义的网络。