Nonlinear functional analysis
Morse theory is a branch of nonlinear functional analysis.
Nonlinear functional analysis is a branch of Mathematical Analysis that deals with nonlinear mappings.
Topics
Its subject matter includes:[1]:1–2
- generalizations of calculus to Banach spaces
- implicit function theorems
- fixed-point theorems (Brouwer fixed point theorem, Fixed point theorems in infinite-dimensional spaces, topological degree theory, Jordan separation theorem, Lefschetz fixed-point theorem)
- Morse theory and Lusternik–Schnirelmann category theory
- methods of complex function theory
Notes
- ↑ Schwartz, Jacob T. (1969). Non-Linear Functional Analysis. New York: Gordon & Breach Science Pub. ISBN 978-0-677-01505-7.