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STRANGE FUNCTIONS IN REAL ANALYSIS 3e(hb) 2017
Author: ALEXANDER KHARAZISHVILI
ISBN: 9781498773140
Year: 2017
Publisher: CRC PRESS
Category: MATHEMATICS
Edition: 3
Format: Hard Cover
Language: English
Pages: 426
 ABOUT THE TITLE
Features
•Demonstrates the usefulness of pathological functions in various questions of real analysis
•Examines the importance of such functions in the process of developing basic concepts of mathematical analysis
Reveals the close and profound connections of pathological (paradoxical) functions with logical and set theoretic foundations of mathematical analysis
•Features many challenging exercises in the text that contain valuable information of the topics covered in the book
Summary
Strange Functions in Real Analysis, Third Edition differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In doing so, the book explores a number of important examples and constructions of pathological functions.

After introducing basic concepts, the author begins with Cantor and Peano-type functions, then moves effortlessly to functions whose constructions require what is essentially non-effective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum.

Finally, the author considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms. On the whole, the book is devoted to strange functions (and point sets) in real analysis and their applications.

Author(s) Bio
Prof. A. Kharazishvili is Professor I. Chavachavadze Tibilisi State University, an author of more than 200 scientific works in various branches of mathematics (set theory, combinatorics and graph theory, mathematical analysis, convex geometry and probability theory). He is an author of several monographs. The author is a member of the Editorial Board of Georgian Mathematical Journal (Heldermann-Verlag), Journal of Applied Analysis (Heldermann-Verlag), Journal of Applied Mathematics, Informatics and Mechanics (Tbilisi State University Press)



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