Essential Topology

Description

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. Introduction....Pages 1-2 Continuous Functions....Pages 3-14 Topological Spaces....Pages 15-34 Topological Properties....Pages 37-53 Deconstructionist Topology....Pages 55-88 Homotopy....Pages 91-116 The Euler Number....Pages 117-126 Homotopy Groups....Pages 127-148 Simplicial Homology....Pages 149-166 Singular Homology....Pages 167-197 More Deconstructionism....Pages 199-214