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

Background. Body mass index (BMI) is a person's weight in kilograms (or pounds) divided by the square of height in meters (or feet). Obesity affects a wide spectrum of age groups, from the young to the elderly, and there are several eye diseases related to obesity like diabetic retinopathy, floppy eyelid syndrome, retinal vein occlusion, stroke-related vision loss, age-related macular degeneration, and possibly, refractive errors. Refractive errors (RE) are optical imperfections related to the focusing ability of the eye and are the main cause of visual impairment which may result in missed education and employment opportunities, lower productivity and impaired quality of life. Aim. The study aimed to find an association between bod

      This piece of research deals with assimilation as one of the phonological processes in the language. It is a trial to give more attention to this important process in English language with deep explanation to its counterpart in Arabic. in addition, this study sheds light on the points of similarities and differences concerning this process in the two languages. Assimilation in English means two sounds are involved, and one becomes more like the other.

     The assimilating phoneme picks up one or more of the features of another nearby phoneme. The English phoneme /n/ has t

Cloud computing is a newly developed concept that aims to provide computing resources in the most effective and economical manner. The fundamental idea of cloud computing is to share computing resources among a user group. Cloud computing security is a collection of control-based techniques and strategies that intends to comply with regulatory compliance rules and protect cloud computing-related information, data apps, and infrastructure. On the other hand, data integrity is a guarantee that the digital data are not corrupted, and that only those authorized people can access or modify them (i.e., maintain data consistency, accuracy, and confidence). This review presents an overview of cloud computing concepts, its importance in many

An excellent reputation earned by initiating and practicing sustainable business practices has additional benefits, of which are reducing environmental incidents and an improvement in operational efficiency as this has the potential to help firms improve on productivity and bring down operating costs. Taken further, with ever-increasing socially and environmentally-conscious investors and the public alike, this act of natural resources management could have a significant implication on market value and income of the practicing firms.

The above proposition has been supported by sustainable business practices literature that is continuously conversing and deliberating upon the impact of efficient resource d

In this work, we focused on studying 1,4-naphthoquinones and their derivatives, and knowing the methods of preparing them using different auxiliary agents and forming derivatives containing heterocyclic rings, active groups and saturated rings containing heterogeneous elements . In addition, due to their strong antibacterial, antifungal and anticancer activity, 1,4-naphthoquinone compounds biological importance and are considered a source of various pharmaceutical compounds.