Elements of Point Set Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of Point Set Topology write by John D. Baum. This book was released on 1991-01-01. Elements of Point Set Topology available in PDF, EPUB and Kindle. Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
A Course in Point Set Topology
A Course in Point Set Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in Point Set Topology write by John B. Conway. This book was released on 2013-11-04. A Course in Point Set Topology available in PDF, EPUB and Kindle. 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.
Point Set Topology
Point Set Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Point Set Topology write by Steven A. Gaal. This book was released on 2009-04-23. Point Set Topology available in PDF, EPUB and Kindle. Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.
Set Topology
Set Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Set Topology write by R. Vaidyanathaswamy. This book was released on 1960-01-01. Set Topology available in PDF, EPUB and Kindle. This introductory text covers the algebra of subsets and of rings and fields of sets, complementation and ideal theory in the distributive lattice, closure function, neighborhood topology, much more. Includes numerous exercises. 1960 edition.
Topology
Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology write by Tai-Danae Bradley. This book was released on 2020-08-18. Topology available in PDF, EPUB and Kindle. A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
