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ECO Ecology --- diversity indices --- ecology --- information indices --- numerical analysis --- vector space

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Vector analysis --- Problems, exercises, etc. --- 512.642 --- -Analyse (wiskunde) --- Vectoranalyse : afgeleiden --- Quaternions --- Vector spaces. Vector space theory --- 512.642 Vector spaces. Vector space theory --- Vectorrekening --- Wiskunde --- 311 --- 514.7 --- Vectoranalyse : integralen --- Algebra, Universal --- Mathematics --- Numbers, Complex --- Spinor analysis --- Vector algebra --- Problems, exercises, etc --- Complex analysis --- -Problems, exercises, etc

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In essence the proceedings of the 1967 meeting in Baton Rouge, the volume offers significant papers in the topology of infinite dimensional linear spaces, fixed point theory in infinite dimensional spaces, infinite dimensional differential topology, and infinite dimensional pointset topology. Later results of the contributors underscore the basic soundness of this selection, which includes survey and expository papers, as well as reports of continuing research.

Topology --- Differential geometry. Global analysis --- Differential topology --- Functional analysis --- Congresses --- Analyse fonctionnnelle --- Geometry, Differential --- Anderson's theorem. --- Annihilator (ring theory). --- Automorphism. --- Baire measure. --- Banach algebra. --- Banach manifold. --- Banach space. --- Bounded operator. --- Cartesian product. --- Characterization (mathematics). --- Cohomology. --- Compact space. --- Complement (set theory). --- Complete metric space. --- Connected space. --- Continuous function. --- Convex set. --- Coset. --- Critical point (mathematics). --- Diagram (category theory). --- Differentiable manifold. --- Differential topology. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dual space. --- Duality (mathematics). --- Endomorphism. --- Equivalence class. --- Euclidean space. --- Existential quantification. --- Explicit formulae (L-function). --- Exponential map (Riemannian geometry). --- Fixed-point theorem. --- Fréchet derivative. --- Fréchet space. --- Fuchsian group. --- Function space. --- Fundamental class. --- Haar measure. --- Hessian matrix. --- Hilbert space. --- Homeomorphism. --- Homology (mathematics). --- Homotopy group. --- Homotopy. --- Inclusion map. --- Infimum and supremum. --- Lebesgue space. --- Lefschetz fixed-point theorem. --- Limit point. --- Linear space (geometry). --- Locally convex topological vector space. --- Loop space. --- Mathematical optimization. --- Measure (mathematics). --- Metric space. --- Module (mathematics). --- Natural topology. --- Neighbourhood (mathematics). --- Normal space. --- Normed vector space. --- Open set. --- Ordinal number. --- Paracompact space. --- Partition of unity. --- Path space. --- Product topology. --- Quantifier (logic). --- Quotient space (linear algebra). --- Quotient space (topology). --- Radon measure. --- Reflexive space. --- Representation theorem. --- Riemannian manifold. --- Schauder fixed point theorem. --- Sign (mathematics). --- Simply connected space. --- Space form. --- Special case. --- Stiefel manifold. --- Strong operator topology. --- Subcategory. --- Submanifold. --- Subset. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological space. --- Topological vector space. --- Topology. --- Transfinite induction. --- Transfinite. --- Transversal (geometry). --- Transversality theorem. --- Tychonoff cube. --- Union (set theory). --- Unit sphere. --- Weak topology. --- Weakly compact. --- Differential topology - Congresses --- Functional analysis - Congresses --- Topology - Congresses --- Analyse fonctionnelle.

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The purpose of this book is to provide a self-contained account, accessible to the non-specialist, of algebra necessary for the solution of the integrability problem for transitive pseudogroup structures.Originally published in 1981.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Lie algebras. --- Ideals (Algebra) --- Pseudogroups. --- Global analysis (Mathematics) --- Lie groups --- Algebraic ideals --- Algebraic fields --- Rings (Algebra) --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie algebras --- Pseudogroups --- 512.81 --- 512.81 Lie groups --- Ideals (Algebra). --- Lie, Algèbres de. --- Idéaux (algèbre) --- Pseudogroupes (mathématiques) --- Ordered algebraic structures --- Analytical spaces --- Addition. --- Adjoint representation. --- Algebra homomorphism. --- Algebra over a field. --- Algebraic extension. --- Algebraic structure. --- Analytic function. --- Associative algebra. --- Automorphism. --- Bilinear form. --- Bilinear map. --- Cartesian product. --- Closed graph theorem. --- Codimension. --- Coefficient. --- Cohomology. --- Commutative ring. --- Commutator. --- Compact space. --- Complex conjugate. --- Complexification (Lie group). --- Complexification. --- Conjecture. --- Constant term. --- Continuous function. --- Contradiction. --- Corollary. --- Counterexample. --- Diagram (category theory). --- Differentiable manifold. --- Differential form. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Direct sum. --- Discrete space. --- Donald C. Spencer. --- Dual basis. --- Embedding. --- Epimorphism. --- Existential quantification. --- Exterior (topology). --- Exterior algebra. --- Exterior derivative. --- Faithful representation. --- Formal power series. --- Graded Lie algebra. --- Ground field. --- Homeomorphism. --- Homomorphism. --- Hyperplane. --- I0. --- Indeterminate (variable). --- Infinitesimal transformation. --- Injective function. --- Integer. --- Integral domain. --- Invariant subspace. --- Invariant theory. --- Isotropy. --- Jacobi identity. --- Levi decomposition. --- Lie algebra. --- Linear algebra. --- Linear map. --- Linear subspace. --- Local diffeomorphism. --- Mathematical induction. --- Maximal ideal. --- Module (mathematics). --- Monomorphism. --- Morphism. --- Natural transformation. --- Non-abelian. --- Partial differential equation. --- Pseudogroup. --- Pullback (category theory). --- Simple Lie group. --- Space form. --- Special case. --- Subalgebra. --- Submanifold. --- Subring. --- Summation. --- Symmetric algebra. --- Symplectic vector space. --- Telescoping series. --- Theorem. --- Topological algebra. --- Topological space. --- Topological vector space. --- Topology. --- Transitive relation. --- Triviality (mathematics). --- Unit vector. --- Universal enveloping algebra. --- Vector bundle. --- Vector field. --- Vector space. --- Weak topology. --- Lie, Algèbres de. --- Idéaux (algèbre) --- Pseudogroupes (mathématiques)

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This work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann manifold is of importance for the construction of Chern classes of complex vector bundles. The cohomology ring of a Grassmannian is therefore of interest in topology, differential geometry, algebraic geometry, and complex analysis. Wilhelm Stoll treats certain aspects of the complex analysis point of view.This work originated with questions in value distribution theory. Here analytic sets and differential forms rather than the corresponding homology and cohomology classes are considered. On the Grassmann manifold, the cohomology ring is isomorphic to the ring of differential forms invariant under the unitary group, and each cohomology class is determined by a family of analytic sets.

Algebraic geometry --- Differential geometry. Global analysis --- Grassmann manifolds --- Differential forms. --- Grassmann manifolds. --- Invariants. --- Geometry, Differential. --- Géométrie différentielle. --- Differential invariants. --- Invariants différentiels. --- Forms, Differential --- Continuous groups --- Geometry, Differential --- Grassmannians --- Differential topology --- Manifolds (Mathematics) --- Calculation. --- Cohomology ring. --- Cohomology. --- Complex space. --- Cotangent bundle. --- Diagram (category theory). --- Exterior algebra. --- Grassmannian. --- Holomorphic vector bundle. --- Manifold. --- Regular map (graph theory). --- Remainder. --- Representation theorem. --- Schubert variety. --- Sesquilinear form. --- Theorem. --- Vector bundle. --- Vector space. --- Géométrie différentielle. --- Invariants différentiels.