The family of topologies that induce the Euclidean metric space on every time axis and every space axis exhibits no maximal element when partially ordered by the relation “finer than”, as demonstrated in this article. One conclusion and two reflections emerge and are addressed herein: Conclusion: a. Zeeman’s fine topology [1] and Göbel’s extension to arbitrary spacetimes [2] do not exist. Refle...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

A common fixed point result for weakly increasing mappings satisfying generalized contractive type of Zhang in ordered metric spaces are derived.

* Correspondence: radens@beotel. net Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Beograd 11120, Serbia Full list of author information is available at the end of the article Abstract We introduce ordered quasicontractions and g-quasicontractions in partially ordered metric spaces and prove the respective coincidence point and (common) fixed point results. An e...

*Correspondence: [email protected] Faculty of Mathematics and Informatics, Plovdiv University, Plovdiv, 4000, Bulgaria Abstract In this paper, we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory, we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces over a sol...

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.

In 2007, Long-Guang and Xian[3] replaced introduced cone metric spaces. They replaced the set of real numbers by an ordered Banach space in the definition of metric and generalized the notion of metric space. Recently, Ayse Sönemaz [5] proved a cone metric space with a normal cone, of course it has to be strongly minihedral, is paracompact. In this paper we omit the strongly minihedral of cone....

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...