Overview
- Provides a hands-on introduction to main concepts of point-set topology
- Includes over 300 worked exercises presented in detail
- An ideal supplement to a first course on topology
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Keywords
- problem book topology
- worked examples topology
- solutions exercises topology
- metric spaces
- product topology
- connected space
- compact space
- quotient topology
- fundamental group
- open neighborhood
About this book
This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular.
Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group.
Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus.
Authors and Affiliations
About the author
Rafael López is Professor of Mathematics at the University of Granada, Spain, and has taught a wide range of courses at undergraduate and graduate level, including geometry of curves and surfaces, differentiable manifolds, affine geometry, general topology and algebraic topology. His research interests are in differential geometry, elliptic differential equations and general relativity, with a particular focus on surfaces with prescribed curvature, capillary theory and variational problems on physics. He is the author of several textbooks on topology as well as a research monograph on surfaces with constant mean curvature.
Bibliographic Information
Book Title: Point-Set Topology
Book Subtitle: A Working Textbook
Authors: Rafael López
Series Title: Springer Undergraduate Mathematics Series
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Softcover ISBN: 978-3-031-58512-8Due: 26 June 2024
eBook ISBN: 978-3-031-58513-5Due: 26 June 2024
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: VIII, 398
Number of Illustrations: 113 b/w illustrations, 7 illustrations in colour