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Essential Topology [electronic resource] /by Martin D. Crossley.

by Crossley, Martin D [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Undergraduate Mathematics Series: Publisher: London : Springer London, 2005.Edition: 1.Description: X, 224p. 110 illus. online resource.ISBN: 9781846281945.Subject(s): Mathematics | Topology | Mathematics | TopologyDDC classification: 514 Online resources: Click here to access online
Contents:
Continuous Functions -- Topological Spaces -- Topological Properties -- Deconstructionist Topology -- Homotopy -- The Euler Number -- Homotopy Groups -- Simplicial Homology -- Singular Homology -- More Deconstructionism.
In: Springer eBooksSummary: 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.
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Continuous Functions -- Topological Spaces -- Topological Properties -- Deconstructionist Topology -- Homotopy -- The Euler Number -- Homotopy Groups -- Simplicial Homology -- Singular Homology -- More Deconstructionism.

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.

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