Elements of Abstract Analysis (Springer Undergraduate Mathematics Series) - Softcover

From the reviews of the first edition:

BULLETIN OF MATHEMATICS BOOKS

"...an interesting mix of algebra, topology and functional analysis, with chapter titles like Algebraic Structure, Linear Structure, Geometric Structure and Topological Structure."

"Michael O’Searcoid’s book ‘Element of Abstract Analysis’ is a book that deals with the fundamental principles of mathematics in a broad framework of set-theoretic approach. The book is written with a deep insight. ... The contents are conceptually useful to students. ... The book is a nice readable treat for every student of mathematics and is highly recommended for one semester course at M.Sc. level." (Madhu Tiwari, Journal of the Indian Academy of Mathematics, Vol. 25 (1), 2003)

"This book covers the elements of abstract analysis, treated mostly within the context of topological spaces. ... This is a carefully written book, starting from set-theoretic axioms, and containing about 180 problems and exercises with hints and solutions. It is an ideal source of information for independent student study. There is a comprehensive index." (European Mathematical Society Newsletter, September, 2002)

"The book presents some concepts of analysis and the mathematical structures which enfold them. ... the reviewer recommends the book to everyone interested in analysis, especially those scholars interested in studying more advanced areas like Functional Analysis, or Operator Theory." (Catalin Badea, Zentralblatt MATH, Vol. 999 (24), 2002)

"The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed ... . It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. This book is a rigorous, self-contained introduction to functional analysis that will also serve as a text on abstract mathematics." (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)

"This is a book about a few elementary concepts of analysis and the mathematical structures which enfold them. ... The book is written specifically for final-year and undergraduate students who should already be familiar with most of the mathematical structures discussed ... and with many of the principal analytical concepts ... . It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics." (Zentralblatt für Didaktik der Mathematik, February, 2002)

While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis.