In this paper, we study the notion of Cauchy-complete preorder in a regular category, following work in [CS86], introducing the logic of a regular category. We give a different, stronger characterization than in loc.cit. for those preorders. Using this, we provide a new construction of the Cauchy-completion in a exact category. AMS Classification: 18A40, 03G30.

We investigate the effect on Cauchy complete objects of the change of base 2-functor V-Cat → W-Cat induced by a two-sided enrichment V → W. We restrict our study to the case of locally partially ordered bases. The reversibility notion introduced in [Wal82] is extended to two-sided enrichments and Cauchy completion. We show that a reversible left adjoint two-sided enrichment F : V → W between lo...

Quasi-nearness biframes provide an asymmetric setting for the study of nearness; in [1] a completion (called a quasi-completion) was constructed for such structures and in [2] completeness was characterized in terms of the convergence of regular Cauchy bifilters. In this talk, questions of functoriality for this quasi-completion are considered and one sees that having enough regular Cauchy bifi...

In this paper, we shall define and study the concept of  -statistical convergence and  -statistical Cauchy in random 2-normed space. We also introduce the concept of  -statistical completeness which would provide a more general frame work to study the completeness in random 2-normed space. Furthermore, we also prove some new results.

We explore the distinction between convergence and absolute convergence of series in both Archimedean and non-Archimedean ordered fields and find that the relationship between them is closely connected to sequential (Cauchy) completeness.

A criterion for a spacelike hypersurface in a conformally stationary spacetime to be a Cauchy hypersurface is given. The criterion is based on the forward and the backward completeness of a non-reversible Finsler metric associated to the hypersurface.

In this paper, we deal with the notion of fuzzy metric space (X,M,∗), or simply X, due to George and Veeramani. It is well known that such spaces, in general, are not completable also there exist p-Cauchy sequences which Cauchy. We prove if every sequence X Cauchy, then principal, observe converse false, general. Hence, introduce study a stronger concept than called strongly principal. Moreover...