In this thesis, we introduce eight types of topologies on a finite digraphs and state the implication between these topologies. Also we studied some pawlak's concepts and generalization rough set theory, we introduce a new types for approximation rough digraphs depending on supra open digraphs. In addition, we present two various standpoints to define generalized membership relations, and state the implication between it, to classify the digraphs and help for measure exactness and roughness of digraphs. On the other hand, we define several kinds of fuzzy digraphs. We also introduce a topological space, which is induced by reflexive graph and tolerance graphs, such that the graph may be infinite. Furthermore, we offered some properties of th

  This research aims to identify the economic design techniques and materials that can be used in the implementation of cosmetic supplements to the spaces of the dwelling. The research relied on the descriptive and analytical approach by describing and analyzing models of design techniques and materials that can be used in the production of cosmetic supplements in the interior spaces of the dwelling.
The results of the research concluded that the beautification of the spaces of the dwelling is one of the necessary and important pieces to add aesthetic touches to the internal spaces, and that the use of economic design techniques and materials contributes to the implementation of many pieces of complementary beautification of the

        In our research, we introduced new concepts, namely ^*and **-light mappings, after we knew ^*and **-totally disconnected mappings through the use of -open sets.

Many examples, facts, relationships and results have been given to support our work.

      Faintly continuous (FC) functions, entitled faintly S-continuous and faintly δS-continuous functions have been introduced and investigated via a -open and -open sets. Several characterizations and properties of faintly S-continuous and faintly -Continuous functions were obtained. In addition, relationships between faintly s- Continuous and faintly S-continuous function and other forms of FC function were investigated. Also, it is shown that every faintly  S-continuous is weakly S-continuous. The Convers is shown to be satisfied only if the co-domain of the function is almost regular.

In this paper, the concept of semi-?-open set will be used to define a new kind of strongly connectedness on a topological subspace namely "semi-?-connectedness". Moreover, we prove that semi-?-connectedness property is a topological property and give an example to show that semi-?-connectedness property is not a hereditary property. Also, we prove thate semi-?-irresolute image of a semi-?-connected space is a semi-?-connected space.

The aim of this paper is to present a weak form of -light functions by using -open set which is -light function, and to offer new concepts of disconnected spaces and totally disconnected spaces. The relation between them have been studied. Also, a new form of -totally disconnected and inversely -totally disconnected function have been defined, some examples and facts was submitted.

The topic of the research tagged (narrative structure and its impact on building open and closed endings in the fictional film) is summarized by studying the mechanism of employing closed and open endings in the fictional film. novelist, then the need for it, as well as the objectives of the research and clarifying its limits as well as its importance. Then moving to the theoretical framework, which included three topics, where the first topic was entitled (the cinematic construction of the film narrative), either the second topic (the structure of complexity and narrative solutions), or the third topic dealt with the subject (the structure of the end and its relationship to the construction of the narrative). After completing the theore

The main purpose of this paper is to study feebly open and feebly closed mappings and we proved several results about that by using some concepts of topological feebly open and feebly closed sets , semi open (- closed ) set , gs-(sg-) closed set and composition of mappings.

  The aim of this paper is to introduce a new type of proper mappings called semi-p-proper mapping by using semi-p-open sets, which is weaker than the proper mapping. Some properties and characterizations of this type of mappings are given.