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The description for this book, Convergence and Uniformity in Topology. (AM-2), Volume 2, will be forthcoming.

Topology. --- Absolute value. --- Abstract algebra. --- Algebraic topology. --- Axiom of choice. --- Binary relation. --- Cardinal number. --- Characteristic function (probability theory). --- Closed set. --- Closure operator. --- Combinatorial topology. --- Compact space. --- Complete lattice. --- Complete metric space. --- Continuous function (set theory). --- Continuous function. --- Countable set. --- Counterexample. --- Dimension theory (algebra). --- Dimension theory. --- Discrete space. --- Domain of a function. --- Empty set. --- Enumeration. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Family of sets. --- Finite set. --- General topology. --- Geometry. --- Hahn–Banach theorem. --- Hausdorff space. --- Homeomorphism. --- Infimum and supremum. --- Integer. --- Interval (mathematics). --- Lebesgue constant (interpolation). --- Limit point. --- Linear space (geometry). --- Mathematician. --- Mathematics. --- Maximal element. --- Metric space. --- Monotonic function. --- Mutual exclusivity. --- Natural number. --- Negation. --- Normal space. --- Open set. --- Ordinal number. --- Real number. --- Regular space. --- Requirement. --- Scientific notation. --- Separation axiom. --- Set (mathematics). --- Set theory. --- Special case. --- Subsequence. --- Subset. --- Suggestion. --- Summation. --- Superspace. --- Theorem. --- Theory. --- Topological algebra. --- Total order. --- Transfinite induction. --- Transfinite number. --- Transfinite. --- Transitive relation. --- Tychonoff space. --- Ultrafilter. --- Uncountable set. --- Uniform continuity. --- Union (set theory). --- Upper and lower bounds. --- Zorn's lemma.

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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

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The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on Riemann surfaces. In fact, the additional structures involved can be considered as local forms of the uniformizations of Riemann surfaces. In this study, Robert Gunning discusses the corresponding pseudogroup structures on higher-dimensional complex manifolds, modeled on the theory as developed for Riemann surfaces.Originally published in 1978.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.

Analytical spaces --- Differential geometry. Global analysis --- Complex manifolds --- Connections (Mathematics) --- Pseudogroups --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Global analysis (Mathematics) --- Lie groups --- Geometry, Differential --- Analytic spaces --- Manifolds (Mathematics) --- Adjunction formula. --- Affine connection. --- Affine transformation. --- Algebraic surface. --- Algebraic torus. --- Algebraic variety. --- Analytic continuation. --- Analytic function. --- Automorphic function. --- Automorphism. --- Bilinear form. --- Canonical bundle. --- Characterization (mathematics). --- Cohomology. --- Compact Riemann surface. --- Complex Lie group. --- Complex analysis. --- Complex dimension. --- Complex manifold. --- Complex multiplication. --- Complex number. --- Complex plane. --- Complex torus. --- Complex vector bundle. --- Contraction mapping. --- Covariant derivative. --- Differentiable function. --- Differentiable manifold. --- Differential equation. --- Differential form. --- Differential geometry. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Elliptic operator. --- Elliptic surface. --- Enriques surface. --- Equation. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Exterior derivative. --- Fiber bundle. --- General linear group. --- Geometric genus. --- Group homomorphism. --- Hausdorff space. --- Holomorphic function. --- Homomorphism. --- Identity matrix. --- Invariant subspace. --- Invertible matrix. --- Irreducible representation. --- Jacobian matrix and determinant. --- K3 surface. --- Kähler manifold. --- Lie algebra representation. --- Lie algebra. --- Line bundle. --- Linear equation. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Manifold. --- Mathematical analysis. --- Mathematical induction. --- Ordinary differential equation. --- Partial differential equation. --- Permutation. --- Polynomial. --- Principal bundle. --- Projection (linear algebra). --- Projective connection. --- Projective line. --- Pseudogroup. --- Quadratic transformation. --- Quotient space (topology). --- Representation theory. --- Riemann surface. --- Riemann–Roch theorem. --- Schwarzian derivative. --- Sheaf (mathematics). --- Special case. --- Subalgebra. --- Subgroup. --- Submanifold. --- Symmetric tensor. --- Symmetrization. --- Tangent bundle. --- Tangent space. --- Tensor field. --- Tensor product. --- Tensor. --- Theorem. --- Topological manifold. --- Uniformization theorem. --- Uniformization. --- Unit (ring theory). --- Vector bundle. --- Vector space. --- Fonctions de plusieurs variables complexes --- Variétés complexes

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Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether. Kollár goes back to the original sources and presents them in a modern context. He addresses three methods for surfaces, and gives a self-contained and entirely elementary proof of a strong and functorial resolution in all dimensions. Based on a series of lectures at Princeton University and written in an informal yet lucid style, this book is aimed at readers who are interested in both the historical roots of the modern methods and in a simple and transparent proof of this important theorem.

Singularities (Mathematics) --- 512.761 --- Geometry, Algebraic --- Singularities. Singular points of algebraic varieties --- 512.761 Singularities. Singular points of algebraic varieties --- Adjunction formula. --- Algebraic closure. --- Algebraic geometry. --- Algebraic space. --- Algebraic surface. --- Algebraic variety. --- Approximation. --- Asymptotic analysis. --- Automorphism. --- Bernhard Riemann. --- Big O notation. --- Birational geometry. --- C0. --- Canonical singularity. --- Codimension. --- Cohomology. --- Commutative algebra. --- Complex analysis. --- Complex manifold. --- Computability. --- Continuous function. --- Coordinate system. --- Diagram (category theory). --- Differential geometry of surfaces. --- Dimension. --- Divisor. --- Du Val singularity. --- Dual graph. --- Embedding. --- Equation. --- Equivalence relation. --- Euclidean algorithm. --- Factorization. --- Functor. --- General position. --- Generic point. --- Geometric genus. --- Geometry. --- Hyperplane. --- Hypersurface. --- Integral domain. --- Intersection (set theory). --- Intersection number (graph theory). --- Intersection theory. --- Irreducible component. --- Isolated singularity. --- Laurent series. --- Line bundle. --- Linear space (geometry). --- Linear subspace. --- Mathematical induction. --- Mathematics. --- Maximal ideal. --- Morphism. --- Newton polygon. --- Noetherian ring. --- Noetherian. --- Open problem. --- Open set. --- P-adic number. --- Pairwise. --- Parametric equation. --- Partial derivative. --- Plane curve. --- Polynomial. --- Power series. --- Principal ideal. --- Principalization (algebra). --- Projective space. --- Projective variety. --- Proper morphism. --- Puiseux series. --- Quasi-projective variety. --- Rational function. --- Regular local ring. --- Resolution of singularities. --- Riemann surface. --- Ring theory. --- Ruler. --- Scientific notation. --- Sheaf (mathematics). --- Singularity theory. --- Smooth morphism. --- Smoothness. --- Special case. --- Subring. --- Summation. --- Surjective function. --- Tangent cone. --- Tangent space. --- Tangent. --- Taylor series. --- Theorem. --- Topology. --- Toric variety. --- Transversal (geometry). --- Variable (mathematics). --- Weierstrass preparation theorem. --- Weierstrass theorem. --- Zero set. --- Differential geometry. Global analysis

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This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other wave energy is directed at the material in question, "imperfections" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry.

Waves --- Scattering (Physics) --- Perturbation (Mathematics) --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Mathematical physics --- Atomic scattering --- Atoms --- Nuclear scattering --- Particles (Nuclear physics) --- Scattering of particles --- Wave scattering --- Collisions (Nuclear physics) --- Particles --- Collisions (Physics) --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Mathematics. --- Scattering --- Acoustic wave equation. --- Acoustic wave. --- Affine space. --- Angular frequency. --- Approximation. --- Asymptotic analysis. --- Asymptotic expansion. --- Banach space. --- Basis (linear algebra). --- Bessel's inequality. --- Boundary value problem. --- Bounded operator. --- C0-semigroup. --- Calculation. --- Characteristic function (probability theory). --- Classical physics. --- Codimension. --- Coefficient. --- Continuous function (set theory). --- Continuous function. --- Continuous spectrum. --- Convolution. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dirac delta function. --- Dirichlet problem. --- Distribution (mathematics). --- Duhamel's principle. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Electromagnetism. --- Equation. --- Existential quantification. --- Exponential function. --- Floquet theory. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fredholm integral equation. --- Frequency domain. --- Helmholtz equation. --- Hilbert space. --- Initial value problem. --- Integral equation. --- Integral transform. --- Integration by parts. --- Inverse problem. --- Inverse scattering problem. --- Lebesgue measure. --- Linear differential equation. --- Linear map. --- Linear space (geometry). --- Locally integrable function. --- Longitudinal wave. --- Mathematical analysis. --- Mathematical physics. --- Metric space. --- Operator theory. --- Ordinary differential equation. --- Orthonormal basis. --- Orthonormality. --- Parseval's theorem. --- Partial derivative. --- Partial differential equation. --- Phase velocity. --- Plane wave. --- Projection (linear algebra). --- Propagator. --- Quantity. --- Quantum mechanics. --- Reflection coefficient. --- Requirement. --- Riesz representation theorem. --- Scalar (physics). --- Scattering theory. --- Scattering. --- Scientific notation. --- Self-adjoint operator. --- Self-adjoint. --- Series expansion. --- Sine wave. --- Spectral method. --- Spectral theorem. --- Spectral theory. --- Square-integrable function. --- Subset. --- Theorem. --- Theory. --- Time domain. --- Time evolution. --- Unbounded operator. --- Unitarity (physics). --- Vector space. --- Volterra integral equation. --- Wave function. --- Wave packet. --- Wave propagation.