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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.

Topology --- Topologie --- Analysis situs --- Position analysis --- Rubber-sheet geometry

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Topologie générale, Chapitres 5 à 10 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce deuxième volume du Livre de Topologie générale, troisième Livre du traité, décrit de nombreux outils fondamentaux en topologie et en analyse, tels que le théorème d’Urysohn, le théorème de Baire ou les espaces polonais. Il comprend les chapitres : Groupes à un paramètre ; Espaces numériques et espaces projectifs ; Les groupes additifs Rn ; Nombres complexes ; Utilisation des nombres réels en topologie générale ; Espaces fonctionnels. Il contient également des notes historiques. Ce volume a été publié en 1974.

Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear

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Topology --- Topologie --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear

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Topology --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear

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Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Topology.