The present paper is primarily concerned with the study of L-guilds in an L-merotopic space. It is shown that every L-cluster is an L-guild; however the converse is not true. For contigual and regular L-merotopies, where on one side we gave an example of a space, which is neither contigual nor binary, on the other side we constructed L-merotopic spaces that are contigual and binary. It is shown...

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 paper studies the category theoretic aspects of ε-approach nearness spaces and ε-approach merotopic spaces, respectively, ε ∈ (0,∞], which are useful in measuring the degree of nearness (resemblance) of objects. Such structures measure the almost nearness of two collections of subsets of a nonempty set. The categories εANear and εAMer are shown to be full supercategories of various well-kn...

Abstract This article considers the problem of how to formulate a framework for the study of the nearness of tolerance rough sets (TRS). The solution to the problem stems from recent work on near sets and approach spaces as well as from the realisation that disjoint TRSs can be viewed in the context of approach merotopic spaces. A set of TRSs equipped with a distance function satisfying certain...

The categorical topologists Bentley et al. [1] have shown that the category FIL of filter spaces is isomorphic to the category of filter merotopic spaces which were introduced by Katětov [3]. The category CHY of Cauchy spaces is also known to be a bireflective, finally dense subcategory of FIL [7]. So the category FIL is an important category which deserves special discussion. A completion theo...

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...

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...