We investigate the behaviour of split extensions in category $OrdGrp$ (pre)- ordered groups. Namely we show that lexicographic order plays a key role on existence compatible orders for semidirect products, establishing necessary and sufficient conditions such existence; prove Split Short Five Lemma holds (stably) strong extensions, identify classes which admit classifier.

this paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. the classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

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...

Abstract We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined between preordered normed spaces. The is accomplished by introducing Lagrange multiplier theorem dual program with variables that pointed closed processes. nature assumed the processes essential derivation main results presented in this research...

Properties of preordered monoids are investigated and important subclasses such structures studied. The corresponding full subcategories related between them by appropriate functors as well with the categories sets monoids. Schreier split extensions described in subcategory whose preorder is determined positive cone.

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

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 this paper, a certain new connectedness of l-fuzzy subsets inl-topological spaces is introduced and studied by means of preclosed sets. itpreserves some fundamental properties of connected set in general topology.especially the famous k. fan’s theorem holds.