We clarify and discuss a misunderstanding between uniform completeness metric that has appeared in the literature study on Alexandrov topology for spacetime.

We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper “A Proposal for Revisiting Banach Caristi Type Theorems b-Metric Spaces”. also characterize the completeness of b-metric spaces with help variant contractivity condition introduced authors aforementioned article.

Metric spaces can be generalized to partial metric spaces. Partial have a unique concept related distance. In usual case, there is no distance from two same points. But, we obtain the points in It means that not absolutely zero. Using basic of spaces, find analogy between and We define d^p formed by p, with applying characteristics metric. At beginning, implement determine sequences L_2 (P). th...

Temporal logic has been successfully used for modeling and analyzing the behavior of reactive and concurrent systems. Standard temporal logic is inadequate for real-time applications because it only deals with qualitative timing properties. This is overcome by metric temporal logics which offer a uniform logical framework in which both qualitative and quantitative timing properties can be expre...

Temporal logic has been successfully used for modeling and analyzing the behavior of reactive and concurrent systems. One shortcoming of (standard) temporal logic is that it is inadequate for real-time applications, because it only deals with qualitative timing properties. This is overcome by metric temporal logics which ooer a uniform logical framework in which both qualitative and quantitativ...

A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As appli...

1.3. De nition. ABSTRACT. We apply enriched category theory to study Cauchy completeness in continuity spaces. Our main result is the equivalence in continuity spaces of the category theoretic and the uniform notions of Cauchy completeness. This theorem, which generalizes a result of Lawvere for quasi-metric spaces, makes a natural connection between the category-theoretic and topological aspec...

This talk will deal to a certain extent with the natural continuation of some work in progress that was introduced last year at the Spanish Relativity Meeting in Salamanca 1, 2 and that has recently been published 3. The reason for investigating geodesic completeness of Lorentzian manifolds is twofold. From the mathematical point of view, there is no analogue for the Hopf-Rinow theorem that cha...

The aim of the present paper is to prove that the family of all closed nonempty subsets of a complete probabilistic metric space L is complete with respect to the probabilistic Pompeiu-Hausdorff metric H . The same is true for the families of all closed bounded, respectively compact, nonempty subsets of L. If L is a complete random normed space in the sense of Šerstnev, then the family of all n...