An Introduction to Naïve Set Theory and Its Applications

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.

Introduction.- Functions and Relations.- Ordinal and Cardinal Numbers.- Applications in Other Branches of Mathematics.- Banach-Tarski Paradox.

S.M. Srivastava is Emeritus Professor at the Statistics and Mathematics Unit, Indian Statistical Institute (ISI), Kolkata, West Bengal, India, which he joined in 1980. He is also Visiting Professor at the Indian Association for the Cultivation of Science, Kolkata, West Bengal, India. He graduated from the ISI Kolkata, in 1980, under the supervision of Prof. A. Maitra. He was a member of the Institute for Advanced Studies, Princeton, during the academic year 1979–1980. His primary research interest lies in descriptive set theory. He is the recipient of the Indian National Science Academy medal for young scientists. Author of the books, A Course on Borel Sets and A Course on Mathematical Logic (both published by Springer), he is an enthusiastic teacher and has written several expository articles aimed at popularising mathematical logic and set theory in India.