Categories of lax (T, V )-algebras are shown to have pullbackstable coproducts if T preserves inverse images. The general result not only gives a common proof of this property in many topological categories but also shows that important topological categories, like the category of uniform spaces, are not presentable as a category of lax (T, V )-algebras, with T preserving inverse images. Moreov...

Near sets are disjoint sets that resemble each other. Resemblance is determined by considering set descriptions defined by feature vectors (n-dimensional vectors of numerical features that represent characteristics of objects such as digital image pixels). Near sets are useful in solving problems based on human perception [44, 76, 49, 51, 56] that arise in areas such as image analysis [52, 14, ...

Krasner hyperrings are a generalization of rings. Indeed, in hyperring the addition is hyperoperation, while multiplication an ordinary operation. On other hand, rough set theory near theory. Now, this paper we interested combining these concepts. We study and investigate notion on nearness approximation space. Also, define subhyperring, hyperideal, homomorphism prove some results present sever...

In this article we present some mappings which can be used to measure the degree of inclusion of a set in a set and which characterize the binary relation of being-near-to, defined on finite sets of objects in line with Peters, Skowron, and Stepaniuk [12]. By means of these mappings, called inclusion functions in general, we extend the notion of nearness to the graded case where one can measure...

The theory of formal spaces and the more recent theory of apartness spaces have a priori not much more in common than that each of them was initiated as a constructive approach to general topology. We nonetheless try to do the first steps in relating these competing theories to each other. Formal topology was put forward in the mid 1980s by Sambin [11] in order to make available to Martin–Löf’s...