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Decompositions of manifolds

Manifolds (Mathematics) --- Decomposition (Mathematics) --- Mathematics --- Probabilities --- Geometry, Differential --- Topology --- 515.16 --- 515.16 Topology of manifolds --- Topology of manifolds

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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.

Topology --- Topological spaces. --- Dimension theory (Topology) --- Dimension theory (Topology). --- Topological spaces --- Spaces, Topological --- 515.12 --- 515.12 General topology --- General topology

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This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written accounts of each topic. Because a number of the sources are rather inaccessible to students, the second part of the book comprises a collection of some of these classic expositions, from journals, lecture notes, theses and conference proceedings. They are connected by short explanatory passages written by Professor Adams, whose own contributions to this branch of mathematics are represented in the reprinted articles.

Algebraic topology. --- Topology --- Algebraic topology --- #KVIV --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- 515.14 --- 515.14 Algebraic topology --- Algèbre homologique. --- Algebra, Homological --- Topologie algébrique --- Topologie algébrique

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Homotopy theory: an introduction to algebraic topology

Algebraic topology --- Homotopy theory --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- 515.14 --- Deformations, Continuous --- Topology --- 515.14 Algebraic topology --- Homotopy theory. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Mathematical Theory --- Topologie algebrique --- Homotopie --- Homologie et cohomologie

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If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language. The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set-theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate students can benefit from some parts. Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In some points, the book treats its material differently than other texts on the subject: * Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; * Nets are used extensively, in particular for an intuitive proof of Tychonoff's theorem; * A short and elegant, but little known proof for the Stone-Weierstrass theorem is given.

Geometry. --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematics --- Euclid's Elements --- Algebraic topology. --- Algebraic Topology. --- Topology --- 515.12 --- 515.12 General topology --- General topology