Essential Topology (repost) - ISBN:1852337826

Essential Topology (repost)

Date: 12 November 2010, 04:16

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Martin D. Crossley, "Essential Topology"
Springer | 2005 | ISBN: 1852337826 | 224 pages | PDF | 3,1 MB

Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, 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, reflecting the fact that these are often the key examples behind current research.
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.
Review
"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)

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