Illustrated Introduction to Topology and Homotopy

This self-contained book explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. It takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs. Requiring only some familiarity with group theory, the text incorporates nearly 600 figures as well as various examples that show how the theory can be applied. It also includes roughly 750 exercises, many of which are relatively new.

List of contents

TOPOLOGY: Sets, Numbers, Cardinals, and Ordinals. Metric Spaces: Definition, Examples, and Basics. Topological Spaces: Definition and Examples. Subspaces, Quotient Spaces, Manifolds, and CW-Complexes. Products of Spaces. Connected Spaces and Path Connected Spaces. Compactness and Related Matters. Separation Properties. Urysohn, Tietze, and Stone-Čech. HOMOTOPY: Isotopy and Homotopy. The Fundamental Group of a Circle and Applications. Combinatorial Group Theory. Seifert-van Kampen Theorem and Applications. On Classifying Manifolds and Related Topics. Covering Spaces, Part 1. Covering Spaces, Part 2. Applications. Applications in Group Theory. Bibliography.

About the author

Sasho Kalajdzievski

Product details

• Authors: Sasho Kalajdzievski, Sasho (University of Manitoba Kalajdzievski, Kalajdzievski Sasho
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 24.03.2015
• EAN: 9781439848159
• ISBN: 978-1-4398-4815-9
• No. of pages: 488
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > General, dictionaries; MATHEMATICS / General, SCIENCE / Physics / Mathematical & Computational, MATHEMATICS / Geometry / General, MATHEMATICS / Functional Analysis, geometry, Mathematical physics, Calculus & mathematical analysis, Applied mathematics, Calculus and mathematical analysis, Mathematical / Computational / Theoretical physics