Elements of Topology

Theory and Practice
2. Auflage 2026
ISBN: 978-1-041-21683-4
Verlag: Taylor & Francis Ltd

Buch, Englisch, 264 Seiten, Format (B × H): 178 mm x 254 mm

Reihe: Textbooks in Mathematics

This book is an ambitious but optimistic treatment of the subject of topology. Not only does it treat the standard basic material about point-set topology, it also gives an introduction to algebraic topology, a treatment of manifolds, a discussion of function spaces, some ideas of knot theory, a presentation of graph theory, and some ideas from dynamical systems. Even the exciting new topic of the Jones polynomial is covered.

After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in several areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures.

Topic coverage has been reduced in this edition, and exercise sets have been added at the end of each section. The book as a whole—and the first two chapters in particular— offer many examples. Solutions to odd-numbered exercises are included at the end.

Today’s students need a text that speaks to them in their own language, and at a pace with which they are comfortable. That is the goal of this edition. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.

Zielgruppe

Undergraduate Advanced

Autoren/Hrsg.

Krantz, Steven G.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

1. Fundamentals  2. Advanced Properties  3. Basic Algebraic Topology  4. Manifold Theory  5. Function Spaces  6. Knot Theory

Über Autor(innen)

Steven G. Krantz is a professor at Washington University in St. Louis where he teaches mathematics. He has previously taught at UCLA, Princeton University, and Penn State University. He received his Ph.D. from Princeton University in 1974. Krantz has directed 20 Ph.D. students and 8 Masters students. He has published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize. He is a Fellow of the American Mathematical Society.