We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

This article considers the problem of how approach spaces can be used in the study of near filters, in general, and descriptively near filters, in particular. The solution to the problem stems from recent work on approach spaces, approach merotopies, near filters, descriptively near sets, and a specialised form of merotopy defined in terms of a variation of the C̆ech gap functional in measuring ...

Bi ideals are the generalisation of quasi ideals. In this article, it is defined that notion bi-ideals in semirings on weak nearness approximation spaces. Afterwards, explained some concepts and definitions related to subject. Also, given definition m-bi (m,n)-quasi Thus, we examine relationship between .

This article considers the problem of how to formulate a framework for the study of the nearness of collections of subsets of a set (also more tersely termed families of a set). The solution to the problem stems from recent work on approach spaces, near sets, and a specialised form of gap functional. The collection of all subsets of a set equipped with a distance function is an approach space.

This article introduces quasi-ideals in semirings on weak nearness approximation spaces. Concepts and definitions are given to clarify the subject of quasi ideals Some basic properties also given. Furthermore, it is that definition upper-near ideals. And, examined relationship between upper near Therefore, features described this study will contribute greatly theoretical development theory.

In order to improve the validity and accuracy of fault diagnosis on mechanical equipment, this study applies fuzzy nearness approach by adjusting the traditional formulations. Besides, it points out the disadvantages in fault diagnosis of traditional nearness approach based on experimental data of gear transmission. A fuzzy nearness functionbased model is constructed to execute the fault diagno...

We provide a fairly general method, which is straightforward and widely applicable, for constructing some coreflections in the category of nearness frames. The method captures all coreflective subcategories with 1 1 coreflection maps; this includes the well-known uniform, totally bounded and separable coreflections. The primary application of this method answers in the affirmative the question ...

A first—order axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for constructive topology.

Nearness (a fuzzy nearness) is a fuzzy relation that can be used to model various grades of “being close” in a linear space. We study the uniform convergence of a sequence of functions with values in a space equipped with a nearness relation. The uniform convergence for the mappings into a space with a fuzzy nearness is defined and it is shown that a theorem similar to Moore-Osgood theorem for ...

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...