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Register a new userExistence of Free Groups and Semigroups in Some Kinds of Compactification
وجود الزمر الحرة و أنصاف الزمر الحرة في بعض أنواع الرص
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من المعروف أن المجموعة (Z×Z) هي نصف زمرة بالنسبة لعملية الجمع، حيث Z مجموعة الأعداد الصحيحة. فإذا زودناها بالتبولوجيا المتقطعة (القوية), فإنها تصبح فضاء تبولوجيا منتظمًا تمامًا، و من ثم يوجد لها رص ستون.شك.
It is known that (Z×Z) is a semigroup with respect to addition, and it can be endowed with the discrete topology; where Z is the set of integers. We can make β(Z×Z), the Stone –Cech compactification of (Z×Z), a right – topological semi group (Baker & Butcher).
References used
Walker, R. C. ١٩٧٤. The Stone – Cech compactification. Springer – Verlag. Berlin, Heidelberg, New York
Buther, R. J. ١٩٧٥. “The Stone–Cech compactification of a toplogical semigroup, and its algebra of measures. Ph.D. thesis, University of Sheffield
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يرتبط الإطار الرياضي لميكانيك الكم ارتباطاً وثيقاً بما يصفه علماء الرياضيات بنظريةتمثيل الزمر , درسنا في بحثنا هذا هذه الفكرة ببعض التفصيل
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