Sets and orderings: sets; functions; relations and orderings; more about sups and infs; sets of sets - filters topologies; 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: toplogical 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.
Key Features * Covers some hard-to-find results including: * Bessagas and Meyers converses of the Contraction Fixed Point Theorem * Redefinition of subnets by Aarnes and Andenaes * Ghermans characterization of topological convergences * Neumanns nonlinear Closed Graph Theorem * van Maarens geometry-free version of Sperners Lemma * Includes a few advanced topics in functional analysis * Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user * Has its own webpage: http://math.vanderbilt.edu/
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/
This is quite a book! From the table of contents, it would appear to include just about everything one would want to know about the foundations of analysis. It is well-organized and the exposition in the sample chapters is quitegoodclear, concise, and relatively easy to read. It is very good technically; the author knows what he is talking about. --George L. Cain, GEORGIA INSTITUTE OF TECHNOLOGY At the very outset, I would like to say that I am very much impressed by what I have seen. I have read the Preface and understood the authors purpose and his aims. I admire him for his courage in attempting such a daunting task, and I admire him even more for what appears to me to be a very successful completion of this task.....I am very excited over the prospect of this book being made available; it will be a very useful reference not only for beginning graduate students, but also for their teachers. --Robert G. Bartle, EASTERN MICHIGAN UNIVERSITY