This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.
Contents:
- Principles of Set Theory and Mathematical Logic
- Metric and Topological Spaces
- Homotopy Theory
- Measure Spaces
- Linear Spaces
- Manifolds and Fiber Bundles
- Topological Methods in Nonlinear Analysis
- Variational Analysis in the Large
- Mathematical Modelling of the Physical Space-Time
Readership: Mathematical physicists.
