Essential Topology

This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research. The book is ideal for self-study.


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.

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

Inhalt
Continuous Functions.- Topological Spaces.- Topological Properties.- Deconstructionist Topology.- Homotopy.- The Euler Number.- Homotopy Groups.- Simplicial Homology.- Singular Homology.- More Deconstructionism.

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