CiNii 図書 - Categorical topology : proceedings of the International Conference, Berlin, August 27th to September 2nd, 1978

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.

Coordinate Systems and Vectors.- Differentiation.- Integration.- Vectors.- Infinite Series.- Integrals and Series as Functions.- Dirac Delta Functions.- Vector Analysis.- Complex Arithmetic.- Complex Analysis.- Differential Equations.- Laplace's Equation.- Other PDEs of Mathematical Physics.- Nonlinear Dynamics.- Probabilities.- Tensors.- Index.

巻冊次: : Berlin ISBN 9783540095033

Recovering a space from its banach sheaves.- Completeness is productive.- Legitimacy of certain topological completions.- On E-normal spaces.- Two procedures in bitopology.- Saks spaces and vector valued measures.- A question in categorical shape theory: When is a shape-invariant functor a kan extension?.- The finest functor preserving the baire sets.- Lifting closed and monoidal structures along semitopological functors.- On non-simplicity of topological categories.- Kan Lift-extensions in C.G. Haus.- Topological functors from factorization.- Groupoids and classification sequences.- Concentrated nearness spaces.- Initial and final completions.- Algebra ? topology.- Topological spaces admitting a "Dual".- Special classes of compact spaces.- Pairs of topologies with same family of continuous self-maps.- Hereditarily locally compact separable spaces.- Injectives in topoi, I: Representing coalgebras as algebras.- Injectives in Topoi, II: Connections with the axiom of choice.- Categories of statistic-metric spaces.- A categorical approach to primary and secondary operations in topology.- Limit-metrizability of limit spaces and uniform limit spaces.- Banach spaces over a compact space.- A note on (E,M)-functors.- Convenient topological algebra and reflexive objects.- Existence and applications of monoidally closed structures in topological categories.- Connection properties in topological categories and related topics.- On projective and injective objects in some topological categories.- An embedding characterization of compact spaces.- Connection and disconnection.- Connections between convergence and nearness.- Functors on categories of ordered topological spaces.- On the coproduct of the topological groups ? and ?2.- Lifting semifinal liftings.- Normally supercompact spaces and convexity preserving maps.- Structure Functors.- Function spaces in topological categories.

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Categorical topology : proceedings of the International Conference, Berlin, August 27th to September 2nd, 1978

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