Date of Award
2005
Document Type
Thesis
Degree Name
Master of Arts in Mathematics
Department
Mathematics
Abstract
A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.
Recommended Citation
Peske, Wendy Ann, "A topological approach to nonlinear analysis" (2005). Theses Digitization Project. 2779.
https://scholarworks.lib.csusb.edu/etd-project/2779
