by N K Laos (University of Kent, UK)

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.

• 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