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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

The duration of the contract is a legal term first provided for in French Amendment Decree No. 131/2016, and given the increasing importance of time in contracts, we have chosen to study the legal rules governing time at the formative stage by drawing on changes in French law compared to both Iraqi and Egyptian laws. Article 1102 of French Amendment Decree No. 131/2016 stipulates that: "Everyone is free to contract or not to contract, to choose the person with whom he contracts, and to determine the content and form of the contract within the limits established by law." Contractual freedom does not permit a breach of the rules relating to public order), as well as article 1104, which provides for (contracts must be nego

The aim of this study is to identify the effect of enabling the effectiveness of the work of the audit committees in private commercial banks and to identify the extent of awareness of the importance of empowerment in the work of these committees, especially as it is known that these committees, especially the inspection committees that go to private banks and from various sources including committees of the Central Bank of Iraq Committees of the Securities Commission and finally committees of the external audit offices, through an analysis of the determinants of empowerment in the performance of the most important work of the audit committees, namely: supervising the process of preparing reports, supervising the system of intern

    Clopidogrel is a prodrug that must be transformed into an active metabolite by hepatic cytochrome P450 (CYP) isoenzymes to prevent platelet clotting. Polymorphisms of the CYP2C19 gene can cause a reduction or complete loss of CYP2C19 enzyme activity resulting in inhibiting clopidogrel metabolism, effectiveness and increase stroke recurrence risk in ischemic stroke patients. This study aims to investigate the correlation between genetic polymorphisms in CYP2C19*2 and*3 and recurrent risk in patients with ischemic stroke taking clopidogrel 75mg in Kurdistan region –Iraq. This retrospective case-control study was carried out at Kurdistan, Erbil, Medicina medical center, and Rizgary general hospital from January 2021 to

Mercury, arsenic, cadmium and lead, were measured in sediment samples of river and marine environmental of Basra governorate in southern of Iraq. Sixteen sites of sediment were selected and distributed along Shatt Al-Arab River and the Iraqi marine environment. The samples were distributed among one station on Euphrates River before its confluence with Tigris River and Shatt Al-Arab formation, seven stations along Shatt Al-Arab River and eight stations were selected from the Iraqi marine region. All samples were collected from surface sediment in low tide time. ICP technique was used for the determination of mercury and arsenic for all samples, while cadmium and lead were measured for the same samples by using Atomic Absorption Spectrosc