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Fundamentals of advanced mathematics. 2, Field extensions, topology and topological vector spaces, functional spaces, and sheaves /
The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the first volume focused on the formal conditions for...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London, UK : Kidlington, Oxford, UK :
ISTE Press ; Elsevier,
2018.
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| Colección: | New mathematical methos, systems and applications set.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Title page; Table of Contents; Copyright; Preface; Errata for Volume 1; List of Notation; Chapter 1: Field Extensions and Differential Field extensions; Chapter 2: General Topology; Chapter 3: Topological Vector Spaces; Chapter 4: Measure, Integration, Function spaces; Chapter 5: Sheaves; 1: Field Extensions and Differential Field Extensions; Abstract; 1.1 Galois theory; 1.2 Transcendental extensions; 1.3 Differential Galois theory; 1.4 Differentially transcendental extensions; 2: General Topology; Abstract; 2.1 Introduction to general topology; 2.2 Filters and nets.
- 2.3 Topological structures2.4 Uniform structures; 2.5 Bornologies; 2.6 Baire spaces, Polish spaces, Suslin spaces, and Lindel�A�f spaces; 2.7 Uniform function spaces; 2.8 Topological algebra; 3: Topological Vector Spaces; Abstract; 3.1 Introduction; 3.2 General topological vector spaces; 3.3 Locally convex spaces; 3.4 Important types of locally convex spaces; 3.5 Weak topologies; 3.6 Dual of a locally convex space; 3.7 Bidual and reflexivity; 3.8 Additional notes about �a#x84;� and �a#x84;�S-spaces and their duals; 3.9 Continuous multilinear mappings; 3.10 Hilbert spaces; 3.11 Nuclear spaces.
- 4: Measure and Integration, Function SpacesAbstract; 4.1 Measure and integration; 4.2 Functions in a single complex variable; 4.3 Function spaces; 4.4 Generalized function spaces; 5: Sheaves; Abstract; 5.1 Introduction; 5.2 General results about sheaves; 5.3 Sheaves of Modules; 5.4 Cohomology of sheaves; Bibliography; Cited Authors; Index.