This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

Recent growth in transport and wireless communication technologies has aided the evolution of Intelligent Transportation Systems (ITS). The ITS is based on different types of transportation modes like road, rail, ocean and aviation. Vehicular ad hoc network (VANET) is a technology that considers moving vehicles as nodes in a network to create a wireless communication network. VANET has emerged as a resourceful approach to enhance the road safety. Road safety has become a critical issue in recent years. Emergency incidents such as accidents, heavy traffic and road damages are the main causes of the inefficiency of the traffic flow. These occurrences do not only create the congestion on the road but also increase the fuel consumption and p

Crime has become a phenomenon associated with human socialization.  Wherever human groups are found, a crime, which differs from one society to another, is found. It is one of the most dangerous social issues that undermines the solidarity of a given society. This is because it establishes a takeoff from community's norms, values, customs and traditions, and thus turns into a danger to the lives of people, groups and society that threatens its strength and security. The paper focuses on the crimes that violate the social law, like child rape, incest and electronic extortion, which are increasing in size, increasing as a result their repercussions on the human society. The study seeks several objectives, including: examining the natu

Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is a basic pri

The "Nudge" Theory is considered one of the most recent theories, which is clear in the economic, health, and educational sectors, due to the intensity of studies on it and its applications, but it has not yet been included in crime prevention studies. The use of  Nudge theory appears to enrich the theory in the field of crime prevention, and to provide modern, effective, and implementable mechanisms.

The study deals with the "integrative review" approach, which is a distinctive form of research that generates new knowledge on a topic through reviewing, criticizing, and synthesizing representative literature on the topic in an integrated manner so that new frameworks and perspectives are created around it.

The study is bas

Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is

Freedom of opinion is one of the freedoms that constitutions and laws have guaranteed to protect and is exercised through the media. However, this freedom must be exercised within certain limits, which include respecting a person’s right to preserve his privacy, image and reputation. Just as the media has the freedom to exercise its right to publish and express its opinion with complete frankness, it is in return obligated to respect the rights of others and avoid defaming them and violating their privacy. If the media does this, the injured party has the right to demand compensation for the damage he has suffered as a result.

United nation determined many basic climatic effects which affect the crust of Earth.
And the most important one is the climatic change and its effect on environmental, economic,
social, and political effects. So, the amount of rain which is considered as one of climatic
changes in Iraq should be studied.So, this research explains the factors which affect rain, its
overall average, the variation in the amounts of rain, the amount of yearly rain and variation
in both yearly and monthly rains by using standard variation and yearly fluctuation.As a
result, it is concluded that the number of rainy days doesn't mean an increase in rains amount.
And there's variation in rains amount in all study areas which is contrastive

In most recent studies, long-term retention after orthodontic treatment has been hypothesized that may be necessary to maintain the stability of the dentition and avoid post-treatment changes. The bonded fixed retainer is characterized by its clinical effectiveness, patient acceptance, and lack of patient complaints as compared with a removable retainer. An electronic database (such as PubMed, PubMed Central, Web of Science, Science Direct, Cochrane Library, Scopus, and ResearchGate) has been collected using specific keywords. Of the 152 articles, only randomized clinical trials that investigated different types of fixed retainers or compared fixed with removable retainers were illustrated in tables and included in this review. The