Buch, Englisch, 374 Seiten, Format (B × H): 162 mm x 240 mm, Gewicht: 720 g
Buch, Englisch, 374 Seiten, Format (B × H): 162 mm x 240 mm, Gewicht: 720 g
ISBN: 978-0-19-870130-9
Verlag: OXFORD UNIV PR
set, the first of which develops the mathematical structure and the second of which applies it to classical and Relativistic physics.
The book begins with a brief historical review of the development of mathematics as it relates to geometry, and an overview of standard topology. The new theory, the Theory of Linear Structures, is presented and compared to standard topology. The Theory of Linear Structures replaces the foundational notion of standard topology, the open set, with the notion of a continuous line. Axioms for the Theory of Linear Structures are laid down, and definitions of other geometrical notions developed in
those terms. Various novel geometrical properties, such as a space being intrinsically directed, are defined using these resources. Applications of the theory to discrete spaces (where the standard theory of open sets gets little purchase) are particularly noted. The mathematics is developed up
through homotopy theory and compactness, along with ways to represent both affine (straight line) and metrical structure.
Zielgruppe
Mathematicians, physicists, and philosophers
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Topologie
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
- Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik
- Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
- Naturwissenschaften Physik Quantenphysik Relativität, Gravitation
Weitere Infos & Material
Acknowledgments
Introduction
Mathematical Foundations
1: Topology and Its Shortcomings
2: Linear Structures, Neighborhoods, Open Sets
Appendix to Chapter 2
3: Closed Sets, Open Sets (Again), Connected Spaces
4: Separation Properties, Convergence, and Extensions
5: Properties of Functions
6: Subspaces and Substructures; Straightness and Differentiability
7: Metrical Structure
Appendix: A Remark about Minimal Regular Metric Spaces
8: Product Spaces and Fiber Bundles
9: Beyond Continua
Axioms and Definitions
Bibliography