بعض البنى الجديدة على متعدد طيات فريشيه المنتظم
Some New Structures on a Uniform Frechet Manifold
- الباحث
- محمد جبار حسين
- المشرف
- زاهر دبيس النافع
- الجامعة
- جامعة بابل
- الكلية / القسم
- كلية التربية للعلوم الصرفة / الرياضيات
- الشهادة
- دكتوراه
- السنة
- 2022
- لغة الرسالة
- انكليزي
- الكلمات المفتاحية
- Frechet manifold; Uniform Frechet algebras; Differential structures; Infinite dimensional manifolds
Abstract
The present work introduced a new class of differentiability for uniform Frechet algebras using the differential structures of uniform Banach algebras and that through adoption projective limit and it's a consideration that each uniform frechet algebra is a projective limit of a system composed of uniform Banach algebra Where it was done through this method Generalization of many differential and topological structures advance knowledge on uniform Banach algebra be the first (uniform Frechet algebra) is projective limit of component system uniform Banach algebra. A theoretical basis for the study of infinite-dimensional manifolds over algebras is created. A number of theorems are proved, generalizing the classical results of differential calculus in the case of manifolds over algebras. We give here a brief account of this approach, which will be systematically applied. In continuity theory we are concerned with projective method on a linear map between uniform Frechet algebras which makes this map continuous. This theory has been mainly developed in the context of Frechet spaces, and there are excellent accounts of continuity theory. In chapter one, we give Fundamental concepts and basic definitions, which are related to our work are given and supported with many theorems and examples of spaces we needed as requirements for the next chapters. İn chapter two, considered the study of continuity and differentiability on maps between uniform Frechet algebras with the approach of a projective limits continuity and differentiability and this introduces a new class of continuous differentiable which we so-called . In chapter three, we defined and discussed a new smooth manifold, constructed by structures that were investigated in chapter two, and this manifold we so−called manifold of class or - manifold in which is of course smooth manifold. In the last chapter, many topological and differentiable structures are modeled on a - manifolds, like smooth projective structures, tangent spaces, and tangent bundles of the - manifold.
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