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

Graphic design art depends on changeable cognitive systems which their relation and items relying on the accumulation of humane knowledge and thong and the humane look to the venality and his explanation to the relation between him and the venality , then the graphic design art becomes an important item of this accumulation knowledge besides , it is on kind of knowledge kinds . The technological advancement in communication lauds to increasing in communication media and design methods , where the computer and its application in graphic design promotes the design process because of it's capalebities which lead to in creasing in production process , minimizing the cost and time and achieving creative and aesthetic aspect because of it's fe

Iraq is considered one of the countries most susceptible to the negative impacts of climate change. According to international reports, it is classified as among the top five most affected by climate change in the world, leading to economic resource shortages and an increase in water scarcity, which exposes societal stability in Iraq to a threat.  This may result in social disintegration and civil conflicts, so climate changes are considered one of the most dangerous crises affecting societal stability in Iraq during this stage.  In this context, the research attempts to trace the causes of climate change and their effects on societal stability in Iraq and suggest some necessary measures to confront them in the future.  The resea

The Fourth Industrial Revolution represents an advanced stage of technological development, characterized by the integration of digital, physical, and biological technologies, with a strong focus on smart connectivity and advanced data analysis. At the core of this revolution stands Artificial Intelligence (AI), which enables the processing of vast amounts of data, decision-making with speed and accuracy, automation of processes, and enhancement of productivity and quality. This research examines the transformative role of AI in the humanities, particularly in archaeological, historical, and geographical studies, where traditional methods face limitations in handling complex and extensive datasets.The study aims to highlight these l

The activity of Alanine aminopeptidase( AAP ) was measured in the urine of healthy and urinary tract cancer patients , the results showed higher activity of (AAP) in patients compared to healthy . AAP was Purified from the urine of healthy and patients with urinary tract cancer by dialysis and gel filtration (Sephadex G – 50) and two isoenzymes of (AAP) were separated from urine by using ion-exchang resin (DEAE – Sephadex A – 50 ) in previous study. The kinetics studies showed that both isoenzymes I and II obeyed Michaelis – Menton equation . with optimal concentration of alanine-4-nitroanilide as substrate for isoenzymes I and II which was (2 x 10-3 mol/L ). The two isoenzymes obeyed Arrhenius equation up two 37° C and t

The Fourth Industrial Revolution represents an advanced stage of technological development, characterized by the integration of digital, physical, and biological technologies, with a strong focus on smart connectivity and advanced data analysis. At the core of this revolution stands Artificial Intelligence (AI), which enables the processing of vast amounts of data, decision-making with speed and accuracy, automation of processes, and enhancement of productivity and quality. This research examines the transformative role of AI in the humanities, particularly in archaeological, historical, and geographical studies, where traditional methods face limitations in handling complex and extensive datasets.The study aims to highlight these l