Handbook of Analysis and Its Foundations

Eric Schechter obtained his Ph.D. in mathematics at the University of Chicago. He is currently Associate Professor at Vanderbilt University, and has also taught at Duke University. Schechters research focuses on differential equations, fixed point theory, and the Axiom of Choice. He currently resides in Nashville, Tennessee with his wife, Elvira Casal, and his two children. Please visit the web page for hisbook: http://math.vanderbilt.edu/~schectex/ccc/

Sets and Orderings: Sets. Functions. Relations and Orderings. More About Sups and Infs. Filters, Topologies, and Other Sets of Sets. Constructivism and Choice. Nets and Convergences. Algebra: Elementary Algebraic Systems. Concrete Categories. The Real Numbers. Linearity. Convexity. Boolean Algebras. Logic and Intangibles. Topology and Uniformity: Topological Spaces. Separation and Regularity Axioms. Compactness. Uniform Spaces. Metric and Uniform Completeness.Baire Theory. Positive Measure and Integration. Topological Vector Spaces: Norms. Normed Operators. Generalized Riemann Integrals. Frechet Derivatives. Metrization of Groups and Vector Spaces. Barrels and Other Features of TVSs. Duality and Weak Compactness. Vector Measures. Initial Value Problems. References. Subject Index. List of Symbols.