- Features undergraduate material in metric spaces, abstract topological spaces, and continuous real-valued functions
- Develops the material from the more particular to the general concepts
- Contains many exercises of varying difficulty
- Includes interesting historical notes.
This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.
John B. Conway is Professor Emeritus of the Department of Mathematics at The George Washington University. He is the author of other well-regarded textbooks, including but not limited toFunctions of One Complex Variable, A Course in Functional Analysis, and A Course in Operator Theory.
From the book reviews:
“This book by Conway (George Washington Univ.) provides the three stepping-stones for leading a successful practitioner of calculus to proficiency in point set topology, with one chapter devoted to each. … Summing Up: Recommended. Upper-division undergraduates and beginning graduate students.” (F. E. J. Linton, Choice, Vol. 51 (11), July, 2014)
“The book under review is, as the title makes clear, an introduction to point set topology … . Conway wrote this book to give students ‘a set of tools’, discussing ‘material [that] is used in almost every part of mathematics.’ … this is a well-written book that I enjoyed reading. Assuming that your idea of what to teach in a first-semester course in topology is in line with the author’s, this book would make an excellent text for such a course.” (Mark Hunacek, MAA Reviews, January, 2014)
“The author is a specialist in analysis with a life long love for point set topology. … There is a relatively large collection of well investigated biographies which appear as footnotes, which are interesting and helpful, espacially for young readers. … The book will be a success, a good introduction to point set topology and a valuable entrance … .” (Friedrich Wilhelm Bauer, zbMATH, Vol. 1284, 2014)