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Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. For more information on this book, see http://math.vanderbilt.edu/
* 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/
Sets and orderings: sets;
relations and orderings;
more about sups and infs;
sets of sets - filters topologies;
constructivism and choice;
nets and convergences. Algebra: elementary algebraic systems;
the real numbers;
logic and intangibles. Topology and uniformity: toplogical spaces separation and regularity axioms;
metric and uniform completeness;
positive measure and integration. Topological vector spaces: norms;
generalized Riemann integrals;
metrization of groups and vector spaces;
barrels and other features of TVSs;
duality and weak compactness;
initial value problems.
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