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: Green Tea is made from the leaf of the plant “Camellia sinensis”. Green tea is reported to contain thousands of bioactive ingredients including catechins which have shown great promise for having antimicrobial effects. Periodontal diseases represent one of the most prevalent diseases around the world and the main etiologic factor behind it, is plaque accumulation, in addition certain kinds of bacteria have been detected frequently in subjects suffering from periodontitis, Several studies suggested that the outcome of periodontal treatment is better if particular pathogens including Aggregatibacteractinomycetemcomitans can no longer be detected after therapy. Materials and Methods: plaque samples were collected from 2

The Video effect on Youths Value

A laboratory experiment has been carried out in the College of Science-University of Salahaddin to study the effect of different levels (0,5,10 and 15%) and sizes(250 and 1000µm) of walnut seeds residues and (160mg.kg^-1) phosphorus fertilization on the concentration of phosphorus availability and alkaline phosphatase activity in calcareous soil during 15 and 30 days period of incubation, the experimental design in factorial complet randomize design (C.R.D) with three replications. The results indicated that the application of different levels of walnut seed residues decreases the concentration of phosphorus availability and alkaline phosphatase activity, however the results revealed that combination between levels and sizes o

Most of the mosques in the Islamic world fall under specific and known forms and patterns to a large extent, and such patterns have grown and evolved from the few basic and uniform models, but they changed slowly due to the impact with a mixture of changing functional requirements and cultural landscapes because of the variables of time and place to form patterns known and famous in this day across parts of the Islamic world and its borders. There was no exception to these patterns, but small numbers of mosques that were probably the result of personal experiences or improvisational resolutions, or in response to specific or temporary stimuli. However, the emergence of a specific pattern which does not belong to any of these patt

The present study was aimed to find out the role of humoral immunity in the pathogenesis of psoriasis. Complements C3, C4 and immunoglobulin IgE .The study included 55 Iraqi patients with psoriasis 30 (15 females ,15 males) were untreated with any drugs. The other patient group consisted of 25 (9 female and 16 male) treated with a biological treatment (infliximab) ,and 30 (13 males ,12 females) healthy control group. Blood sample were withdrawn (5) ml of venous blood for both patients and members of the control ,to conduct the Immunological tests to determine the quantitative for each of total IgE by using (ELISA) and C3,C4 by Single Radial Immunodiffuse (SIRD). The results showed significant increase in the level of probability (P <0.0