The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

P. aeruginosa is one of the complex targets for antimicrobial chemotherapy. Also, it is intrinsically resistant to several antibiotics. It produces β-lactamases enzymes that are responsible for the widespread β-lactam antimicrobial resistance. There are three major groups of β-lactamase enzymes, MBLs and ESBLs forming Pseudomonas is a major issue for the treatment of burns victims. Methods: A total of 28 clinical isolates related to P. aeruginosa have been obtained from the burns specimens from patients attending to AL-Imam hospital/Baghdad-Iraq, through the period from October 2015 to March 2016. Also, all isolates have been recognized as P. aeruginosa via utilizing bacteriological assay and confirmed by Vitek 2. In addition, the suscep

The main purpose of this paper is to introduce a some concepts in fibrewise bitopological spaces which are called fibrewise , fibrewise -closed, fibrewise −compact, fibrewise -perfect, fibrewise weakly -closed, fibrewise almost -perfect, fibrewise ∗-bitopological space respectively. In addition the concepts as - contact point, ij-adherent point, filter, filter base, ij-converges to a subset, ij-directed toward a set, -continuous, -closed functions, -rigid set, -continuous functions, weakly ijclosed, ij-H-set, almost ij-perfect, ∗-continuous, pairwise Urysohn space, locally ij-QHC bitopological space are introduced and the main concept in this paper is fibrewise -perfect bitopological spaces. Several theorems and characterizations c

         The living urban space is considered one of the most important elements of the success of modern cities, and it is the first mental image that is formed by people (residents and visitors) of the city , a measure of the frequency, presence and interaction of people in the spaces is an indication of the city's vitality, well-being and economic strength .

The occupation of the city of Mosul before the terrorist ISIS in 2014 and the subsequent liberation operations and the end of the war in 2017 had a great impact on the destruction of the old city on the right side and the death of its urban spaces due to the abandonment of people to it, especially the area (Al-Midan and Al-Qalayaat),

            This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2  and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.

In this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given.  For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.

In this article, the partially ordered relation is constructed in geodesic spaces by betweeness property, A monotone sequence is generated in the domain of monotone inward mapping,  a monotone inward contraction mapping is a  monotone Caristi inward mapping is proved, the general fixed points for such mapping is discussed and A mutlivalued version of these results is also introduced.