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Although much has happened in the field since the publication of this book, this single volume on Riemannian geometry and for the analysis and geometry of symmetric spaces still offers a clear overview of the subjects.
Geometry, Differential. --- Generalized spaces. --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Differential geometry
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The description for this book, A Theory of Cross-Spaces. (AM-26), Volume 26, will be forthcoming.
Generalized spaces. --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Addition. --- Adjoint. --- Banach space. --- Big O notation. --- Euclidean space. --- Exponential function. --- Linear space (geometry). --- Notation. --- Sequence. --- Theorem.
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Quantum mechanics. Quantumfield theory --- Mathematical physics --- Quantum theory --- Generalized spaces --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Mathematics --- Generalized spaces. --- Mathematical physics. --- Quantum theory.
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Functional analysis --- General relativity (Physics) --- Generalized spaces. --- Mathematics. --- 519.63 --- Generalized spaces --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Mathematics --- General relativity (Physics) - Mathematics.
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Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.
Banach spaces. --- Generalized spaces. --- Polynomials. --- Banach, Espaces de --- Espaces généralisés --- Polynômes --- Mathematics. --- Functional analysis. --- Geometry. --- Functional Analysis. --- Banach spaces --- Generalized spaces --- Polynomials --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Functional calculus --- Math --- Euclid's Elements --- Calculus of variations --- Functional equations --- Integral equations --- Science
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"Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers is extensively studied in this book. In particular, an exhaustive solution of the "twin paradox" is given, followed by a detailed exposition of space-time geometry and trigonometry. Finally, and appendix on general properties of commutative hypercomplex systems with four unities is presented."--Jacket.
Theory of relativity. Unified field theory --- Topology --- Generalized spaces --- Special relativity (Physics) --- Ether drift --- Mass energy relations --- Relativity theory, Special --- Restricted theory of relativity --- Special theory of relativity --- Relativity (Physics) --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace
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Topological fields. --- Generalized spaces. --- Topology. --- Corps topologiques. --- Espaces généralisés. --- Topologie. --- Corps topologiques --- Espaces généralisés --- Topological fields --- Generalized spaces --- Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Algebraic fields
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Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
Generalized spaces. --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Global differential geometry. --- Group theory. --- Differential Geometry. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Differential geometry. --- Differential geometry
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Measure and integration theory on infinite-dimensional spaces
Generalized spaces. --- Integrals. --- Measure theory. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Calculus, Integral --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Measure theory --- Mesure, Théorie de la --- Calcul intégral --- Mesure, Théorie de la --- Calcul intégral
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The book is devoted to universality problems. A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different topics of Topology such as: universal mappings, dimension theory, action of groups, inverse spectra, isometrical embeddings, and so on.·Universal spaces ·Universal mappings ·Dimension theory ·Actions of groups ·Isometric Universal Spaces
Generalized spaces. --- Topology. --- Mappings (Mathematics) --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics)
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