Based on the authors' courses and lectures, this 2-volume advanced-level text is now available in a single volume. Topics include metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque interval, Hilbert Space and more. Each section contains exercises. Lists of symbols, definitions and theorems. 1957 edition.
Here's a sample of other books in this Dover category
General Theory of Functions and Integration by Angus E. Taylor Lucid introduction to abstract theories in analysis. Classical theory of points in Euclidean space, continuous functions, ideas of topology, more. For graduate students. 38 diagrams. Introduction. List of Special Symbols. Index.
Theory of Functions, Parts I and II by Konrad Knopp Handy one-volume edition. Part I considers general foundations of theory of functions; Part II stresses special and characteristic functions. Proofs given in detail. Introduction. Bibliographies.
Approximation of Elliptic Boundary-Value Problems by Jean-Pierre Aubin A marriage of the finite-differences method with variational methods for solving boundary-value problems, this self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis.
Set Theory and the Continuum Hypothesis by Paul J. Cohen This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.
Algebras of Holomorphic Functions and Control Theory by Amol Sasane Accessible, undergraduate-level text illustrates the role of algebras of holomorphic functions in the stabilization of a linear control system. Concise, self-contained treatment avoids advanced mathematics. 2009 edition.
Geometry and Convexity: A Study in Mathematical Methods by Paul J. Kelly, Max L. Weiss This text assumes no prerequisites, offering an easy-to-read treatment with simple notation and clear, complete proofs. From motivation to definition, its explanations feature concrete examples and theorems. 1979 edition.
