This study involves new notions of continuity mapping between quasi-cone metrics spaces (QCMSs), cone metric (CMSs), and vice versa. The relation all were thoroughly studied supported with the help examples. In addition, these continuities compared various types two QCMSs. are

Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its d-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower sem...

We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings ...

The domain theoretic notion of lifting allows one to extend a partial order in a trivial way by a minimum. In the context of Quantitative Domain Theory (e.g. [BvBR98] and [FK93]) partial orders are represented as quasi-metric spaces. For such spaces, the notion of the extension by an extremal element turns out to be non trivial. To some extent motivated by these considerations, we characterize ...

For any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤d, the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences) X, is introduced and studied.We observe that its induced quasi-uniformity is finer than the quasi-uniformity of pointwise convergence and weaker than the quasi-uniformity o...

In his well-known paper dealing with the construction of the injective hull of a metric space Isbell introduced the concept of an endpoint of a (compact) metric space. In the present article we introduce similarly the notion of an endpoint in a (joincompact) T0-quasi-metric space. It turns out that in a (joincompact) T0-quasi-metric space there is a dual concept which we shall call a startpoint...

A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric: it can be thought of as an asymmetric metric. Quasi-metrics were first introduced in 1930s and are a subject of intensive research in the context of topology and theoretical computer science. The central result of this thesis, developed in Chapter 3, is that a natural correspondence exists betwee...

The notion of dislocated quasi metric space was initiated by F. M. Zeyada, G. H. Hassan and M. A. Ahmed[18] in 2006. It is a generalization due to P. Hitzler and A. K. Seda[7] in dislocated metric. Dislocated quasi metric space differs from d islocated metric space with symmetric property. After the establishment of d islocated quasi metric space, it has emerged as important area of research ac...

Extending the well-known result that every fuzzy metric space, in the sense of Kramosil and Michalek, has a completion which is unique up to isometry, we show that every KM-fuzzy quasi-metric space has a bicompletion which is unique up to isometry, and deduce that for each KM-fuzzy quasi-metric space, the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced...