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An Illustrated Introduction to Topology and Homotopy by Sasho Kalajdzievski; CRC Press.; Taylor & Francis is a book available to read on EtoBox.

What is An Illustrated Introduction to Topology and Homotopy about?

An Illustrated Introduction to Topology and Homotopy 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. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs. The first part of the text covers basic topology, ranging from metric spaces and the axioms of topology through subspaces, product spaces, connectedness, compactness, and separation axioms to Urysohns lemma, Tietzes theorems, and Stone-ech compactification. Focusing on homotopy, the second part starts with the notions of ambient isotopy, homotopy, and the fundamental group. The book then covers basic combinatorial group theory, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The last three chapters discuss the theory of covering spaces, the Borsuk-Ulam theorem, and applications in group theory, including various subgroup theorems. Requiring only some familiarity with group theory, the text includes a large number of figures as well as various examples that show how the theory can be applied. Each section starts wit

Author

Sasho Kalajdzievski; CRC Press.; Taylor & Francis

Publisher

Chapman and Hall/CRC

Published

2015

Language

EN

ISBN

9781439848142

Subjects

Science, Mathematics, Physics