This paper is devoted to the discussion the relationships of connectedness between some types of graphs (resp. digraph) and Gm-closure spaces by using graph closure operators.

We define and study new ideas of fibrewise topological space namely fibrewise multi-topological space . We also submit the relevance of fibrewise closed and open topological space . Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space . Furthermore, we propose and prove a number of statements about these ideas. On the other hand, extend separation axioms of ordinary topology into fibrewise setting. The separation axioms are said to be fibrewise multi-T0. spaces, fibrewise multi-T1spaces, fibrewise multi-R0 spaces, fibrewise multi-Hausdorff spaces, fibrewise multi-functionally Hausdorff spaces, fibrewise multi-regular spaces, fibrewise multi-completely regular spaces, fibrewise multi-normal

In this paper we introduce a lot of concepts in bitopological spaces which are ij-ω-converges to a subset, ij-ω-directed toward a set, ij-w-closed functions, ij-w-rigid set, ij-w-continuous functions and the main concept in this paper is ij-w-perfect functions between bitopological spaces. Several theorems and characterizations concerning these concepts are studied.

It is general known that any design in various fields such as the interior design in the field of spaces interior for the public and specific buildings that is concern about the use of humans resident , as well as other considerations relating to the organization of design elements and lines of locomotors activity and the validity of appropriate receiving to provide comfort and achieve the requirements of the position in the space of restaurants field of research.
The researcher choose the title of this study (processors design career in public spaces), the analytical study of the spaces of restaurants, as one of the public spaces that are running in their general environment of people in various strata , ages and other levels , whic

In this paper, we procure the notions of neutrosophic simply b-open set, neutrosophic simply b-open cover, and neutrosophic simply b-compactness via neutrosophic topological spaces. Then, we establish some remarks, propositions, and theorems on neutrosophic simply

b-compactness. Further, we furnish some counter examples where the result fails.

Naturally available products have been used widely for centuries in handling human disease. The present study aimed to determine the effect of aluminum potassium sulfate addition into the soft liner on tensile strength and peel bond strength. The effect of aluminum potassium sulfate evaluated by two methods, first one include incorporation of KAL (SO4)2 into soft liner monomer in concentration (2%,3% by wt.) while the second method include immersion of soft liner specimens in solution of KAL(SO4)2 in concentration(5%,10% percent) during time periods (0,10 minutes). In conclusions, the results of current study encourage use KAL (SO4)2 within soft liner material

In this work , we study different chaotic properties of the product space on a one-step shift of a finite type, as well as other spaces. We prove that the product  is Lyapunove  â€“unstable if and only if at least one  or  is Lyapunove  â€“unstable. Also, we show that and locally everywhere onto (l.e.o)  if and only if is locally everywhere onto (l.e.o) .

         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),