The aim of this paper is to introduce the concept of N  and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.

The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined and studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pairwise pseudo and pairwise Uryshon) - fs bicsp's are introduced and studied in both ech fuzzy soft bi-closure space and their induced fuzzy soft bitopological spaces. It is shown that hereditary property is satisfied for , with respect to ech fuzzy soft bi-closure space but for other mentioned types of separations axioms, hereditary property satisfies for closed subspaces of ech fuzzy soft bi-closure space.

Comes interest in the subject matter in the selection of the Family industry globally as one of the important industries which have developed a clear and significant in recent years, to look at these products and designs to their functional importance have appeared in recent years, the phenomenon of the small spaces because of housing Population density showed the need to find a spare Furniture fit these small spaces On this basis, determine the objective of this research is to arrive at a design techniques for dual-family employee for small spaces research sample included a double family manufactured in laboratories industry Furniture in Baghdad and local research sample includes family double Decker.Research focused on the first four c

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.

The goal of this article is to construct fibrewise w-compact (resp. locally w-compact) spaces. Some related results and properties of these concepts will be investigated. Furthermore, we investigate various relationships between these concepts and three classes of fibrewise w-separation axioms.

The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators

The current research deals with studying the aesthetics of symbolic values in the design of internal spaces and their connotations through their existence as a material value, as well as the symbolic meanings and their connotations that touch the spiritual and emotional side of the human being as an intangible value, and the research included four chapters, so the research problem was embodied by the following question (What is the role of values Symbolism and aesthetics in the design of interior spaces)? Therefore, the aim was to clarify the role of symbolic values and their aesthetics in the design of internal spaces. The first chapter included the importance of research, the need for it, the limits of the research and its terminology.

 In this paper, we introduce  and  study  new  classes of soft  open  sets  in soft bitopological spaces called soft  (1,2)*-omega  open  sets  and  weak forms of soft (1,2)*-omega open sets such as soft  (1,2)*-α-ω-open sets, soft  (1,2)*-pre-ω-opensets, soft  (1,2)*-b-ω-open sets,  and  soft  (1,2)*-β-ω-open  sets. Moreover; some basic properties and the relation among these concepts and other concepts also have been studied.

The research is marked by (Development Design Interior spaces for children's theater halls in the city of Baghdad). Which consists of four chapters, namely, the first chapter the research problem and the need for him, which included identifying the research problem and of poor achievement of aesthetic values and functional at the scene of the child and its significance in that it is a way of cultural entertainment education of the child and its objectives as it aims to evelop interiors for children's theater, and its limits. Theater Magic Lantern in the city of Baghdad, the second chapter addressed the theoretical framework, which consists of the psychology of the child, and space Children's Theatre and types, forms of children's theater

The formal integration of the interior spaces in general and the commercial spaces of the watch shops in the large commercial centers in particular is the goal that the designers aim to reach in order for the interior space to become successful in terms of the design idea and its characteristics. Implementation mechanism. One of the reasons for achieving formal integration in the interior spaces of watch shops is the requirements of the design that must be available in these spaces to reach a state of formal integration between the interior and the exterior so that the space becomes fully integrated in all respects. Because of the aforementioned reasons for dealing with the research, through four chapters: The first chapter included the