Srivastava S. An Introduction to Naive Set Theory and Its Applications 2024

Textbook in PDF format

Primarily designed for graduate students of mathematics, this textbook delves into Naïve set theory, offering valuable insights for senior undergraduate students and researchers specializing in set theory. Commencing with a comprehensive exploration of functions and relations, the book extends its coverage to various applications of Naïve set theory across multiple mathematical branches, including real analysis, linear and abstract algebra, general topology, and introductory aspects of complex analysis and measure theory. The text meticulously introduces cardinal and ordinal numbers, along with transfinite induction, following the natural progression discovered by Cantor during his examination of trigonometric series. While this book provides a solid foundation, students intrigued by set theory for its intrinsic value should recognize that the subject extends far beyond the scope of this text.
Preface.
Introduction.
Functions and Relations.
More on Cardinals and Ordinals.
Applications in Other Branches of Mathematics.
Banach–Tarski Paradox.
Preliminary Concepts and Terminologies from Logic.
Zermelo–Fraenkel Set Theory.
Index