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Graduate Texts in Mathematics: Introduction to Topological Manifolds (Softcover)
"This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically with minimal prerequisites and plenty of geometric intuition." — From the back cover
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VERY GOOD: This book is in very good condition, showing only slight signs of use and wear. It was printed on acid-free paper.
This book is Number 202 in Springer’s Graduate Texts in Mathematics series.
Continued from the back cover: “A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the world ‘manifold.’ Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields.
“In his beautifully conceived Introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics. Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout.”
- Topological Spaces
- New Spaces from Old
- Connectedness and Compactness
- Simplicial Complexes
- Curves and Surfaces
- Homotopy and the Fundamental Group
- Circles and Spheres
- Some Group Theory
- The Seifert-Van Kampen Theorem
- Covering Spaces
- Classification of Coverings
Appendix: Review of Prerequisites
- Set Theory
- Metric Spaces
- Group Theory
The book concludes with References and Index.
- Lee, John M.
- Publish Date:
- 2000 (First Printing)
- Weight (pounds):
- Dimensions (W”xL”xH”):
- Grade Level:
- Springer Graduate Texts in Mathematics
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