Overview
- Unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study
- Written from a thoroughly modern perspective: every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation
- Ideal for self-study; it assumes only a familiarity with the notion of continuity and basic algebra
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (11 chapters)
Keywords
About this book
Taking a direct route, "Essential Topology" brings the most important aspects of modern topology within reach of a second-year undergraduate student. It begins with a discussion of continuity and, by way of many examples, leads to the celebrated "Hairy Ball theorem" and on to homotopy and homology: the cornerstones of contemporary algebraic topology.
While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting examples that clarify the ideas and motivate the student.
With chapters on: continuity and topological spaces; deconstructionist topology; the Euler number; homotopy groups including the fundamental group; simplicial and singular homology, and fibre bundles.
"Essential Topology" contains enough material for two semester-long courses, and offers a one-stop-shop for undergraduate-level topology, leaving students motivated for postgraduate study in the field, and well-prepared for it.
Reviews
From the reviews:
"This book presents the most important aspects of modern topology, essential subjects of research in algebraic topology … . The book contains all the key results of basic topology and the focus throughout is on providing interesting examples that clarify the ideas and motivate the student. … this book contains enough material for two-semester courses and offers interesting material for undergraduate-level topology, motivating students for post-graduate study in the field and giving them a solid foundation." (Corina Mohorianu, Zentralblatt MATH, Vol. 1079, 2006)
"This text provides a concise and well-focused introduction to point set and algebraic topology. The main purpose is to quickly move to relevant notions from algebraic topology (homotopy and homology). Throughout the book the author has taken great care to explain topological concepts by well-chosen examples. It is written in a clear and pleasant style and can certainly be recommended as a basis for an introductory course on the subject." (M. Kunzinger, Monatshefte für Mathematik, Vol. 152 (1), 2007)
Authors and Affiliations
Bibliographic Information
Book Title: Essential Topology
Authors: Martin D. Crossley
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/1-84628-194-6
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Limited 2005
Softcover ISBN: 978-1-85233-782-7Published: 05 August 2005
eBook ISBN: 978-1-84628-194-5Published: 02 February 2006
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: X, 224
Number of Illustrations: 110 b/w illustrations