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Faisceaux, Théorie des. --- Prolongement analytique. --- WKB, Approximation. --- Sheaf theory. --- Analytic continuation. --- WKB approximation.

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Duality theory (Mathematics) --- Isomorphisms (Mathematics) --- Sheaf theory. --- Homotopy theory. --- Faisceaux, Théorie des. --- Isomorphismes (mathématiques) --- Homotopie. --- Dualité, Principe de (mathématiques)

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Algebraic geometry --- Bundeltheorie --- Cohomology [Sheaf ] --- Faisceaux [Théorie des ] --- Invarianten --- Invariants --- Sheaf cohomology --- Sheaf theory --- Sheaves (Algebraic topology) --- Sheaves [Theory of ] --- Théorie des faisceaux

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Anneaux (Algèbre) --- Bundeltheorie --- Cohomology [Sheaf ] --- Faisceaux [Théorie des ] --- Localisatie-theorie --- Localisation [Theorie de la ] --- Localization theory --- Ringen (Algebra) --- Rings (Algebra) --- Sheaf cohomology --- Sheaf theory --- Sheaves (Algebraic topology) --- Sheaves [Theory of ] --- Théorie des faisceaux --- Localization theory. --- Sheaf theory. --- RINGS (Algebra)

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This book is primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems." Sheaves play several roles in this study. For example, they provide a suitable notion of "general coefficient systems." Moreover, they furnish us with a common method of defining various cohomology theories and of comparison between different cohomology theories. The parts of the theory of sheaves covered here are those areas impor­tant to algebraic topology. Sheaf theory is also important in other fields of mathematics, notably algebraic geometry, but that is outside the scope of the present book. Thus a more descriptive title for this book might have been Algebraic Topology from the Point of View of Sheaf Theory. Several innovations will be found in this book. Notably, the con­cept of the "tautness" of a subspace (an adaptation of an analogous no­tion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The fact that sheaf-theoretic cohomology satisfies 1 the homotopy property is proved for general topological spaces. Also, relative cohomology is introduced into sheaf theory. Concerning relative cohomology, it should be noted that sheaf-theoretic cohomology is usually considered as a "single space" theory.

Sheaf theory --- Théorie des faisceaux --- Algebraic topology --- Topologie algébrique --- Faisceaux, Théorie des --- Algebra. --- Algebraic topology. --- Algebraic Topology. --- Topology --- Mathematics --- Mathematical analysis --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Topologie algebrique --- Homologie et cohomologie