in this paper, some recent results established by marin borcut [m. borcut, tripled fixed point theorems for monotone mappings in partially ordered metric spaces, carpathian j. math. 28, 2 (2012), 207--214] and [m. borcut, tripled coincidence theorems for monotone mappings in partially ordered metric spaces, creat. math. inform. 21, 2 (2012), 135--142] are generalized and improved, with much sho...

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...

In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...

5 Goguen’s category of V-sets whose objects are functions with values in a pre-ordered set and morphisms are suitable maps is shown to be a topological construct if and only if the pre-ordered set is a complete lattice; in particular the category Set(L) of L-sets, 7 also considered by Goguen, is topological over Set. The special case when the considered pre-ordered set is L with the “mapping to...

‎ in the present article‎, ‎we study some categorical properties of the category {$bf‎ cpo_{sep}$-$s$} of all {separately strict $s$-cpo's}; cpo's equipped with‎ a compatible right action of a separately strict cpo-monoid $s$ which is‎ strict continuous in each component‎. ‎in particular‎, we show that this category is reflective and coreflective in the‎ category of $s$-cpo's‎, ‎find the free a...

in this paper, some categorical properties of the category ${bf cpo}_{{bf act}text{-}s}$ of all {cpo $s$-acts}, cpo's equipped with actions of a monoid $s$ on them, and strict continuous action-preserving maps between them is considered. in particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. also, we show that the forgetful functor from...

Earlier work by several authors has focused on defining Boolean function classes by means of functional equations. In [10], it was shown that the classes of Boolean functions definable by functional equations coincide with initial segments of the quasi-ordered set (Ω,≤) made of the set Ω of Boolean functions, suitably quasi-ordered. Furthermore, the classes defined by finitely many equations co...

The paper focuses on three problems of generalizing properties of concatenation structures (ordered structures with a monotonic operation) to ordered structures lacking any operation. (1) What is the natural generalization of the idea of Archimedeaness, of commensurability between large and small? (2) What is the natural generalization of the concept of a unit concatenation structure in which t...

In this paper we prove that the collection of all weakly distributive lattice ordered groups is a radical class and that it fails to be a torsion class.

Residuated structures are important lattice-ordered algebras both for mathematics and for logics; in particular, the development of lattice-valued mathematics and related non-classical logics is based on a multitude of lattice-ordered structures that suit for many-valued reasoning under uncertainty and vagueness. Extended-order algebras, introduced in [10] and further developed in [1], give an ...