أثبت في هذا البحث أن حاصل جمع فضائين جزئيين مغلقين للنهاية المعكوسة لفـضاءات شـعاعية
منتهية البعد، هو أيضاً فضاء جزئي مغلق .
كما تم إثبات أن كل مثالي I مغلق للنهاية المعكوسة لجبور لي نصف بسيطة L له فضاء متمم وحيد.
We prove that the sum A + B of closed subspaces A and B of the inverse
limit of finite dimensional vector spaces, V = limVn (n ∈ N) over an
algebraically closed field of characteristic 0 is closed.
We extend also the basic fact that every ideal of a finite dimensional
semisimple Lie algebra has a unique complement to the case of closed ideals of
prosemisimple Lie algebras.
References used
Bourbaki, N. (1989), ''General Topology'', Chapters 1-4, Springer-Verlag
Hochschild, G. and Mostow, G. D. (1957), ''Representations and Representative functions of Lie Groups'', Ann. Of Math 66, 495-542
Humphreys, J. E. (1972), ''Introduction to Lie algebras and representation theory''. Second printing, Springer-Verlag
We extend the well Known Levi-Malcev decomposition theorem of finite
dimensional Lie algebras to the case of pro-finite dimensional Lie algebras
L = limLn (n ∈ N). We also prove that every finite dimensional
homomorphic image of the Cartesian product of finite dimensional nilpotent
Lie algebras is also nilpotent.
The thesis topic discusses the geometry of subspaces of Riemann spaces, and it is a work prepared for obtaining a master's degree in mathematics.
Our study falls into three chapters that include a reference study and then a study of the immersion issue and the geometry of subspaces from Riemann spaces.
In this paper we introduced new types of open and closed sets in bitopological
spaces, where we have introduced the definition of open
sets.
مفهوم التابع لعدة متحولات
التمثيل البياني لتابع لمتحولين
نهايات التوابع لمتحولين واستمرارها
النهايات
النهايات التكرارية
الاستمرار
المشتقات الجزئية
التفاضل التام
التفاضل التام من المراتب العليا
الجاكوبي (Jacobian)
التوابع الشعاعية (Vec
A class of complex differential spaces is defined in a natural way. The
notions of smooth mapping, tangent vectors and vector fields on these spaces
are introduced, so that the fundamental notions in differential geometry can be
formulated.