Schechter E. Handbook of Analysis and Its Foundations 1996 Rep torrent

Textbook in PDF format

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.
Key Features
Covers some hard-to-find results including:
Bessaga's and Meyer's converses of the Contraction Fixed Point Theorem.
Redefinition of subnets by Aarnes and Andenaes.
Gherman's characterization of topological convergences.
Neumann's nonlinear Closed Graph Theorem.
van Maaren's geometry-free version of Sperner's 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.
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 TVS's
Duality and Weak Compactness
Vector Measures
Initial Value Problems.
Index and Symbol List