A Course in Point Set Topology

The ideal text for students of point set topology who are still mastering the art of writing proofs, this course book begins with specialized material, and then extrapolates the general principles. Useful appendices link the material to courses in analysis.

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.

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

Autorentext
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 to Functions of One Complex Variable, A Course in Functional Analysis, and A Course in Operator Theory.

Inhalt
Metric Spaces.- Topological Spaces.- Continuous Real-Valued Functions.- Appendix.- Bibliography.- Terms.- Symbols.